Pertanyaan

Tentukan lima suku pertama dari barisan di bawah ini. h. U n = ( 4 n − 3 ) ( 2 n − 1 ) 1

Tentukan lima suku pertama dari barisan di bawah ini.

h. $U_{n} = \frac{1}{( 4 n - 3 ) ( 2 n - 1 )}$

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M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Perhatikan perhitungan berikut! Jadi, lima suku pertama dari barisan tersebut adalah .

$begin mathsize 14px style U subscript n equals fraction numerator 1 over denominator left parenthesis 4 n minus 3 right parenthesis left parenthesis 2 n minus 1 right parenthesis end fraction end style$

Perhatikan perhitungan berikut!

$begin mathsize 12px style n equals 1 rightwards arrow U subscript 1 equals fraction numerator 1 over denominator open parentheses 4 open parentheses 1 close parentheses minus 3 close parentheses open parentheses 2 open parentheses 1 close parentheses minus 1 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses 4 minus 3 close parentheses open parentheses 2 minus 1 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses 1 close parentheses open parentheses 1 close parentheses end fraction equals 1 end style$

$begin mathsize 12px style n equals 2 rightwards arrow U subscript 2 equals fraction numerator 1 over denominator open parentheses 4 open parentheses 2 close parentheses minus 3 close parentheses open parentheses 2 open parentheses 2 close parentheses minus 1 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses 8 minus 3 close parentheses open parentheses 4 minus 1 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses 5 close parentheses open parentheses 3 close parentheses end fraction equals 1 over 15 end style$

$begin mathsize 12px style n equals 3 rightwards arrow U subscript 3 equals fraction numerator 1 over denominator left parenthesis 4 open parentheses 3 close parentheses minus 3 right parenthesis left parenthesis 2 open parentheses 3 close parentheses minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 12 minus 3 right parenthesis left parenthesis 6 minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 9 right parenthesis left parenthesis 5 right parenthesis end fraction equals 1 over 45 end style$

$begin mathsize 12px style n equals 4 rightwards arrow U subscript 4 equals fraction numerator 1 over denominator left parenthesis 4 open parentheses 4 close parentheses minus 3 right parenthesis left parenthesis 2 open parentheses 4 close parentheses minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 16 minus 3 right parenthesis left parenthesis 8 minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 13 right parenthesis left parenthesis 7 right parenthesis end fraction equals 1 over 91 end style$

$begin mathsize 12px style n equals 5 rightwards arrow U subscript 5 equals fraction numerator 1 over denominator left parenthesis 4 open parentheses 5 close parentheses minus 3 right parenthesis left parenthesis 2 open parentheses 5 close parentheses minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 20 minus 3 right parenthesis left parenthesis 10 minus 1 right parenthesis end fraction equals fraction numerator 1 over denominator left parenthesis 17 right parenthesis left parenthesis 9 right parenthesis end fraction equals 1 over 153 end style$

Jadi, lima suku pertama dari barisan tersebut adalah .