Pertanyaan

k = 1 ∑ n ( 3 k − 2 ) = …

$k = 1 \sum n (3 k - 2) = \dots$

$fraction numerator 3 n minus 2 over denominator n end fraction$

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Habis dalam

Klaim

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat bahwa maka berdasarkan persamaan diatas dan definisi notasi sigma, didapatkan Perhatikan bahwa Sehingga Oleh karena itu, jawaban yang benar adalah D.

Ingat bahwa

sum from n equals a to b of open parentheses x subscript n minus y subscript n close parentheses equals sum from n equals a to b of x subscript n minus sum from n equals a to b of y subscript n

maka berdasarkan persamaan diatas dan definisi notasi sigma, didapatkan

sum from k equals 1 to n of left parenthesis 3 k minus 2 right parenthesis equals sum from k equals 1 to n of 3 k minus sum from k equals 1 to n of 2 equals stack 3 sum with k equals 1 below and n on top k minus 2 n

Perhatikan bahwa

$table attributes columnalign right center left columnspacing 0px end attributes row cell sum from k equals 1 to n of k end cell equals cell 1 plus 2 plus 3 plus 4 plus horizontal ellipsis plus n end cell row cell sum from k equals 1 to n of k end cell equals cell S subscript n end cell row blank equals cell fraction numerator n cross times left parenthesis n plus 1 right parenthesis over denominator 2 end fraction end cell row blank equals cell fraction numerator n squared plus n over denominator 2 end fraction end cell end table$

Sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell stack 3 sum with k equals 1 below and n on top k minus 2 n end cell equals cell 3 open parentheses fraction numerator n squared plus n over denominator 2 end fraction close parentheses minus 2 n end cell row blank equals cell fraction numerator 3 n squared plus 3 n over denominator 2 end fraction minus 2 n end cell row blank equals cell fraction numerator 3 n squared plus 3 n minus 4 n over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 n squared minus n over denominator 2 end fraction end cell row blank equals cell 1 half n left parenthesis 3 n minus 1 right parenthesis end cell end table$

Oleh karena itu, jawaban yang benar adalah D.