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Bentuk sederhana dari i = − 2 ∑ 5 ​ 2 i + j = − 5 ∑ 2 ​ 2 j + k = 2 ∑ 9 ​ 2 k adalah ....

Bentuk sederhana dari  adalah ....

  1. sum from i equals negative 5 to 2 of 2 to the power of i

  2. 55 over 8 sum from i equals negative 5 to 2 of 2 to the power of i

  3. 3 sum from i equals negative 2 to 5 of 2 to the power of i

  4. 137 over 8 sum from i equals negative 2 to 5 of 2 to the power of i

  5. 2 sum from i equals 2 to 9 of 2 to the power of i

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D. Natalia

Master Teacher

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jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

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Pembahasan

Ingat bahwa pada notasi sigma, berlaku perubahan batas bawah dan batas atas sebagai berikut! Oleh karena itu, didapat perhitungan sebagai berikut. Dengan demikian, bentuk sederhana dari adalah . Jadi, jawaban yang tepat adalah D.

Ingat bahwa pada notasi sigma, berlaku perubahan batas bawah dan batas atas sebagai berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals m to n of U subscript i end cell equals cell sum from i equals m plus p to n plus p of U subscript i minus p end subscript end cell row cell sum from i equals m to n of U subscript i end cell equals cell sum from i equals m minus p to n minus p of U subscript i plus p end subscript end cell end table

Oleh karena itu, didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from i equals negative 2 to 5 of 2 to the power of i plus sum from j equals negative 5 to 2 of 2 to the power of j plus sum from k equals 2 to 9 of 2 to the power of k end cell row blank equals cell sum from i equals negative 2 to 5 of 2 to the power of i plus sum from i equals negative 5 to 2 of 2 to the power of i plus sum from i equals 2 to 9 of 2 to the power of i end cell row blank equals cell sum from i equals negative 2 to 5 of 2 to the power of i plus sum from i equals negative 5 plus 3 to 2 plus 3 of 2 to the power of i minus 3 end exponent plus sum from i equals 2 minus 4 to 9 minus 4 of 2 to the power of i plus 4 end exponent end cell row blank equals cell sum from i equals negative 2 to 5 of 2 to the power of i plus sum from i equals negative 2 to 5 of 2 to the power of i minus 3 end exponent plus sum from i equals negative 2 to 5 of 2 to the power of i plus 4 end exponent end cell row blank equals cell sum from i equals negative 2 to 5 of open parentheses 2 to the power of i plus 2 to the power of i minus 3 end exponent plus 2 to the power of i plus 4 end exponent close parentheses end cell row blank equals cell sum from i equals negative 2 to 5 of open parentheses 2 to the power of i open parentheses 1 plus 2 to the power of negative 3 end exponent plus 2 to the power of 4 close parentheses close parentheses end cell row blank equals cell sum from i equals negative 2 to 5 of open parentheses 2 to the power of i open parentheses 1 plus 1 over 8 plus 16 close parentheses close parentheses end cell row blank equals cell sum from i equals negative 2 to 5 of open parentheses 2 to the power of i open parentheses 137 over 8 close parentheses close parentheses end cell row blank equals cell 137 over 8 sum from i equals negative 2 to 5 of 2 to the power of i end cell end table

Dengan demikian, bentuk sederhana dari sum from i equals negative 2 to 5 of 2 to the power of i plus sum from j equals negative 5 to 2 of 2 to the power of j plus sum from k equals 2 to 9 of 2 to the power of k adalah 137 over 8 sum from i equals negative 2 to 5 of 2 to the power of i.

Jadi, jawaban yang tepat adalah D.

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

1

Farhan Maulana

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