Pertanyaan

Hasil dari adalah ....

Hasil dari $begin mathsize 12px style sum from k equals 20 to 60 of open parentheses fraction numerator 4 over denominator open parentheses k minus 2 close parentheses open parentheses k minus 1 close parentheses open parentheses k close parentheses end fraction minus fraction numerator 7 over denominator open parentheses k minus 1 close parentheses open parentheses k close parentheses open parentheses k plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses k close parentheses open parentheses k plus 1 close parentheses open parentheses k plus 2 close parentheses end fraction close parentheses end style$ adalah ....

$begin mathsize 12px style fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 4 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$
$begin mathsize 12px style fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 3 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 4 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$
$begin mathsize 12px style fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction plus fraction numerator 4 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$
$begin mathsize 12px style fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 4 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 3 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$
$begin mathsize 12px style fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$

Y. Pangestu

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Jabarkan bentuk notasi sigmanya untuk melihat polanya. Untuk , maka Untuk , maka Untuk , maka . . . Untuk , maka Untuk , maka Untuk , maka Jika semua hasil penjabaran tersebut dijumlahkan, maka hasilnya adalah Oleh karena itu, diperoleh sebagai berikut. Jadi, jawaban yang tepat adalah B.

Jabarkan bentuk notasi sigmanya untuk melihat polanya.

Untuk k equals 20 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 20 minus 2 close parentheses open parentheses 20 minus 1 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 20 minus 1 close parentheses open parentheses 20 close parentheses open parentheses 20 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 20 close parentheses open parentheses 20 plus 1 close parentheses open parentheses 20 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 20 close parentheses open parentheses 21 close parentheses open parentheses 22 close parentheses end fraction end style$

Untuk k equals 21 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 21 minus 2 close parentheses open parentheses 21 minus 1 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 21 minus 1 close parentheses open parentheses 21 close parentheses open parentheses 21 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 21 close parentheses open parentheses 21 plus 1 close parentheses open parentheses 21 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 20 close parentheses open parentheses 21 close parentheses open parentheses 22 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 21 close parentheses open parentheses 22 close parentheses open parentheses 23 close parentheses end fraction end style$

Untuk k equals 22 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 22 minus 2 close parentheses open parentheses 22 minus 1 close parentheses open parentheses 22 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 22 minus 1 close parentheses open parentheses 22 close parentheses open parentheses 22 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 22 close parentheses open parentheses 22 plus 1 close parentheses open parentheses 22 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 20 close parentheses open parentheses 21 close parentheses open parentheses 22 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 21 close parentheses open parentheses 22 close parentheses open parentheses 23 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 22 close parentheses open parentheses 23 close parentheses open parentheses 24 close parentheses end fraction end style$

Untuk k equals 58 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 58 minus 2 close parentheses open parentheses 58 minus 1 close parentheses open parentheses 58 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 58 minus 1 close parentheses open parentheses 58 close parentheses open parentheses 58 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 58 close parentheses open parentheses 58 plus 1 close parentheses open parentheses 58 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 56 close parentheses open parentheses 57 close parentheses open parentheses 58 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 57 close parentheses open parentheses 58 close parentheses open parentheses 59 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 58 close parentheses open parentheses 59 close parentheses open parentheses 60 close parentheses end fraction end style$

Untuk k equals 59 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 59 minus 2 close parentheses open parentheses 59 minus 1 close parentheses open parentheses 59 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 59 minus 1 close parentheses open parentheses 59 close parentheses open parentheses 59 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 59 close parentheses open parentheses 59 plus 1 close parentheses open parentheses 59 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 57 close parentheses open parentheses 58 close parentheses open parentheses 59 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 58 close parentheses open parentheses 59 close parentheses open parentheses 60 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction end style$

Untuk k equals 60 , maka

$begin mathsize 11px style fraction numerator 4 over denominator open parentheses 60 minus 2 close parentheses open parentheses 60 minus 1 close parentheses open parentheses 60 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 60 minus 1 close parentheses open parentheses 60 close parentheses open parentheses 60 plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 60 plus 1 close parentheses open parentheses 60 plus 2 close parentheses end fraction equals fraction numerator 4 over denominator open parentheses 58 close parentheses open parentheses 59 close parentheses open parentheses 60 close parentheses end fraction minus fraction numerator 7 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$

Jika semua hasil penjabaran tersebut dijumlahkan, maka hasilnya adalah

Oleh karena itu, diperoleh sebagai berikut.

$begin mathsize 12px style sum subscript k equals 20 end subscript superscript 60 open parentheses fraction numerator 4 over denominator open parentheses k minus 2 close parentheses open parentheses k minus 1 close parentheses open parentheses k close parentheses end fraction minus fraction numerator 7 over denominator open parentheses k minus 1 close parentheses open parentheses k close parentheses open parentheses k plus 1 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses k close parentheses open parentheses k plus 1 close parentheses open parentheses k plus 2 close parentheses end fraction close parentheses equals fraction numerator 4 over denominator open parentheses 18 close parentheses open parentheses 19 close parentheses open parentheses 20 close parentheses end fraction minus fraction numerator 3 over denominator open parentheses 19 close parentheses open parentheses 20 close parentheses open parentheses 21 close parentheses end fraction minus fraction numerator 4 over denominator open parentheses 59 close parentheses open parentheses 60 close parentheses open parentheses 61 close parentheses end fraction plus fraction numerator 3 over denominator open parentheses 60 close parentheses open parentheses 61 close parentheses open parentheses 62 close parentheses end fraction end style$

Jadi, jawaban yang tepat adalah B.