Pertanyaan

A B C = = = 1 × 3 + 3 × 5 + 5 × 7 + ⋯ + 97 × 99 1 + 3 + 5 + 7 + ⋯ + 99 1 2 + 3 3 + 5 2 + ⋯ + 9 9 2 Nilai dari A + B + C adalah ....

$A B C = = = 1 \times 3 + 3 \times 5 + 5 \times 7 + \dots + 97 \times 99 1 + 3 + 5 + 7 + \dots + 99 1^{2} + 3^{3} + 5^{2} + \dots + 9 9^{2}$

Nilai dari $A + B + C$ adalah ....

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jumlah dari adalah .

jumlah dari straight A plus straight B plus straight C

adalah

Pembahasan

Ingat sifat notasi sigmaberikut : Perhatikan pola A. Perhatikan pola B. Terdapat kesalahan pada pola C, agar polanya sesuai dengan pola A dan B seharusnya . Perhatikan pola C. Ingat bentuk sigma Dengan demikian, Jadi, jumlah dari adalah .

Ingat sifat notasi sigma berikut :

Perhatikan pola A.

Perhatikan pola B.

Terdapat kesalahan pada pola C, agar polanya sesuai dengan pola A dan B seharusnya C equals 1 squared plus 3 squared plus 5 squared plus... plus 99 squared . Perhatikan pola C.

Ingat bentuk sigma

$table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 1 to n of space i squared end cell equals cell fraction numerator n left parenthesis n plus 1 right parenthesis left parenthesis 2 n plus 1 right parenthesis over denominator 6 end fraction end cell row cell sum from i equals 1 to n of space i end cell equals cell fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end cell end table$

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight A plus straight B plus straight C end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared close parentheses close square brackets minus 49 plus open square brackets sum from n equals 1 to 50 of space 2 n close square brackets minus 50 end cell row blank blank cell plus open square brackets sum from n equals 1 to 50 of space open parentheses 4 n squared minus 4 n close parentheses close square brackets space plus 50 end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared close parentheses close square brackets plus open square brackets sum from n equals 1 to 50 of space 2 n close square brackets plus open square brackets sum from n equals 1 to 50 of space open parentheses 4 n squared minus 4 n close parentheses close square brackets end cell row blank blank cell negative 49 end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared close parentheses close square brackets plus open square brackets sum from n equals 1 to 50 of space open parentheses 2 n plus 4 n squared minus 4 n close parentheses close square brackets minus 49 end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared close parentheses close square brackets plus open square brackets sum from n equals 1 to 50 of space open parentheses 4 n squared minus 2 n close parentheses close square brackets minus 49 end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared close parentheses close square brackets plus open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared minus 2 n close parentheses close square brackets end cell row blank blank cell plus open parentheses 4 times 50 squared minus 2 times 50 close parentheses minus 49 end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 4 n squared plus 2 n plus 4 n squared minus 4 n close parentheses close square brackets end cell row blank blank cell plus left parenthesis 10.000 minus 100 minus 49 right parenthesis end cell row blank equals cell open square brackets sum from n equals 1 to 49 of space open parentheses 8 n squared minus 2 n close parentheses close square brackets plus 9.851 end cell row blank equals cell 8 open parentheses sum from n equals 1 to 49 of space n squared close parentheses minus 2 open parentheses sum from n equals 1 to 49 of space n close parentheses plus 9.851 end cell row blank equals cell 8 open parentheses fraction numerator 49 left parenthesis 49 plus 1 right parenthesis left parenthesis 2 times 49 plus 1 right parenthesis over denominator 6 end fraction close parentheses minus 2 open parentheses fraction numerator 49 left parenthesis 49 plus 1 right parenthesis over denominator 2 end fraction close parentheses end cell row blank blank cell plus 9.851 end cell row blank equals cell 8 open parentheses fraction numerator 49 times 50 times 99 over denominator 6 end fraction close parentheses minus 2 open parentheses fraction numerator 49 times 50 over denominator 2 end fraction close parentheses plus 9.851 end cell row blank equals cell 8 open parentheses fraction numerator 242.550 over denominator 6 end fraction close parentheses minus 2 open parentheses fraction numerator 2.450 over denominator 2 end fraction close parentheses plus 9.851 end cell row blank equals cell 8 left parenthesis 40.425 right parenthesis minus 2.450 plus 9.851 end cell row blank equals cell 323.400 minus 2.450 plus 9.851 end cell row blank equals cell 330.801 end cell end table$

Jadi, jumlah dari straight A plus straight B plus straight C adalah 330.801 .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

1.0 (1 rating)

Falakhgenz Genz

Pembahasan terpotong

Pertanyaan serupa

Jika u 1 = 2 ; u 2 = 4 ; u 3 = 6 ; u 4 = 8 ; dan u 5 = 10 serta v 1 = 1 ; v 2 = 3 ; v 3 = 5 ; v 4 = 7 ; dan v 5 = 9 , maka nilai dari i = 1 ∑ 5 ( u i − 2 v i ) adalah ....

3.0

Jawaban terverifikasi

Nilai dari k = − 2 ∑ 3 k + 3 k 2 = ...

4.8

Jawaban terverifikasi

Diketahui i = 1 ∑ 30 p i = 15 nilai i = 1 ∑ 30 ( 3 − p i ) = ...

4.5

Jawaban terverifikasi

i = 1 ∑ n ( 2 i + 5 ) = n ( n + 6 )

108

0.0

Jawaban terverifikasi