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Pertanyaan

Bentuk sederhana dari 8 n = 4 ∑ 15 ​ n 2 − n = 1 ∑ 12 ​ ( n + 3 ) 2 adalah ....

Bentuk sederhana dari  adalah ....

  1. sum from n equals 1 to 12 of open parentheses 7 n squared plus 42 n plus 61 close parentheses

  2. sum from n equals 1 to 12 of open parentheses 7 n squared plus 42 n plus 63 close parentheses

  3. sum from n equals 1 to 12 of open parentheses 7 n squared minus 42 n plus 61 close parentheses

  4. sum from n equals 1 to 12 of open parentheses 7 n squared minus 42 n plus 63 close parentheses

  5. sum from n equals 1 to 12 of open parentheses 7 n squared plus 42 n minus 63 close parentheses

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

jawaban yang benar adalah B.

Pembahasan

Ingat beberapa aturan dan sifat notasi sigma berikut i) ii) iii) maka berdasarkan sifat dan aturan notasi sigma diatas, didapatkan Oleh karena itu, jawaban yang benar adalah B.

Ingat beberapa aturan dan sifat notasi sigma berikut

i)table attributes columnalign right center left columnspacing 0px end attributes row cell sum from n equals a to b of open parentheses x subscript n minus y subscript n close parentheses end cell equals cell sum from n equals a to b of x subscript n minus sum from n equals a to b of y subscript n end cell row blank rightwards arrow cell sum from n equals a to b of x subscript n minus sum from n equals a to b of y equals sum from n equals a to b of open parentheses x subscript n minus y subscript n close parentheses end cell end table

ii)table attributes columnalign right center left columnspacing 0px end attributes row cell space space sum from n equals a to b of c open parentheses x subscript n close parentheses end cell equals cell c sum from n equals a to b of x subscript n end cell row blank rightwards arrow cell c sum from n equals a to b of x blank subscript n equals sum from n equals a to b of c open parentheses x subscript n close parentheses end cell end table

iii)table attributes columnalign right center left columnspacing 0px end attributes row cell space space sum from n equals a to b of open parentheses x subscript n close parentheses end cell equals cell sum from n equals a minus c to b minus c of x subscript n plus c end subscript end cell end table

maka berdasarkan sifat dan aturan notasi sigma diatas, didapatkan

8 sum from n equals 4 to 15 of n squared minus sum from n equals 1 to 12 of open parentheses n plus 3 close parentheses squared equals 8 sum from n equals 4 minus 3 to 15 minus 3 of left parenthesis n plus 3 right parenthesis squared minus stack sum with n equals 1 below and 12 on top open parentheses n plus 3 close parentheses to the power of 2 end exponent equals 8 sum from n equals 1 to 12 of open parentheses n plus 3 close parentheses squared minus sum from n equals 1 to 12 of open parentheses n plus 3 close parentheses squared equals 7 sum from n equals 1 to 12 of open parentheses n plus 3 close parentheses squared equals sum from n equals 1 to 12 of 7 open parentheses n plus 3 close parentheses squared equals sum from n equals 1 to 12 of 7 open parentheses n squared plus 6 n plus 9 close parentheses equals sum from n equals 1 to 12 of open parentheses 7 n squared plus 42 n plus 63 close parentheses

Oleh karena itu, jawaban yang benar adalah B.

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