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Tentukan nilai penjumlahan dari notasi sigma berikut. b.

Tentukan nilai penjumlahan dari notasi sigma berikut.

b. begin mathsize 14px style sum from p equals 0 to 5 of open parentheses fraction numerator 1 over denominator p plus 1 end fraction plus fraction numerator 1 over denominator p plus 2 end fraction close parentheses end style 

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Jawaban:

Bentuk begin mathsize 14px style sum from p equals 0 to 5 of open parentheses fraction numerator 1 over denominator p plus 1 end fraction plus fraction numerator 1 over denominator p plus 2 end fraction close parentheses end style adalah bentuk sigma yang memiliki batas bawah 0 dan batas atas 5, artinya kita akan membuat deret, dengan mensubstitusikan nilai berurut begin mathsize 14px style p end style dari 0 hingga 5 yaitu begin mathsize 14px style p equals 0 end stylebegin mathsize 14px style p equals 1 end stylebegin mathsize 14px style p equals 2 end stylebegin mathsize 14px style p equals 3 end stylebegin mathsize 14px style p equals 4 end style dan begin mathsize 14px style p equals 5 end style, maka: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from p equals 0 to 5 of open parentheses fraction numerator 1 over denominator p plus 1 end fraction plus fraction numerator 1 over denominator p plus 2 end fraction close parentheses end cell equals cell sum from p equals 0 to 5 of open parentheses fraction numerator p plus 2 plus p plus 1 over denominator left parenthesis p plus 1 right parenthesis left parenthesis p plus 2 right parenthesis end fraction close parentheses end cell row blank equals cell sum from p equals 0 to 5 of open parentheses fraction numerator 2 p plus 3 over denominator left parenthesis p plus 1 right parenthesis left parenthesis p plus 2 right parenthesis end fraction close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from p equals 0 to 5 of open parentheses fraction numerator 2 p plus 3 over denominator left parenthesis p plus 1 right parenthesis left parenthesis p plus 2 right parenthesis end fraction close parentheses end cell equals cell fraction numerator 2 left parenthesis 0 right parenthesis plus 3 over denominator left parenthesis 0 plus 1 right parenthesis left parenthesis 0 plus 2 right parenthesis end fraction plus fraction numerator 2 left parenthesis 1 right parenthesis plus 3 over denominator left parenthesis 1 plus 1 right parenthesis left parenthesis 1 plus 2 right parenthesis end fraction end cell row blank blank cell plus fraction numerator 2 left parenthesis 2 right parenthesis plus 3 over denominator left parenthesis 2 plus 1 right parenthesis left parenthesis 2 plus 2 right parenthesis end fraction plus fraction numerator 2 left parenthesis 3 right parenthesis plus 3 over denominator left parenthesis 3 plus 1 right parenthesis left parenthesis 3 plus 2 right parenthesis end fraction end cell row blank blank cell plus fraction numerator 2 left parenthesis 4 right parenthesis plus 3 over denominator left parenthesis 4 plus 1 right parenthesis left parenthesis 4 plus 2 right parenthesis end fraction plus fraction numerator 2 left parenthesis 5 right parenthesis plus 3 over denominator left parenthesis 5 plus 1 right parenthesis left parenthesis 5 plus 2 right parenthesis end fraction end cell row blank equals cell 3 over 2 plus 5 over 6 plus 7 over 12 plus 9 over 20 plus 11 over 30 plus 13 over 42 end cell row blank equals cell fraction numerator 630 plus 350 plus 245 plus 189 plus 154 plus 130 over denominator 420 end fraction end cell row blank equals cell 1698 over 420 end cell row blank equals cell 283 over 70 end cell end table end style 

Jadi, nilai penjumlahan dari bentuk begin mathsize 14px style sum from p equals 0 to 5 of open parentheses fraction numerator 1 over denominator p plus 1 end fraction plus fraction numerator 1 over denominator p plus 2 end fraction close parentheses end style adalah begin mathsize 14px style 283 over 70 end style 

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