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Question Number 83638 by bshahid010@gmail.com last updated on 04/Mar/20

Answered by TANMAY PANACEA last updated on 05/Mar/20

S=(1/(x+1))+(2/(x^2 +1))+(4/(x^4 +1))+...+(2^n /(x^2^n  +1)) (i think)  S=Σ_(n=0) ^n (2^n /(x^2^n  +1)) total (n+1)terms  S−(1/(x−1))=((1/(x+1))−(1/(x−1)))+(2/(x^2 +1))+(4/(x^4 +1))+..+(2^n /(x^2^n  +1))  S−(1/(x−1))=(((−2)/(x^2 −1))+(2/(x^2 +1)))+(4/(x^4 +1))+..+(2^n /(x^2^n  +1))  s−(1/(x−1))=(((−4)/(x^4 −1))+(4/(x^4 +1)))+..+((2^n /(x^2^n  +1)))  S−(1/(x−1))=(((−8)/(x^8 −1)))+...+((2^n /(x^2^n  +1)))  .....  ......  S−(1/(x−1))=(((−2^(n+1) )/(x^2^(n+1)  −1)))  S=(1/(x−1))−(2^(n+1) /(x^2^(n+1)  −1))

S=1x+1+2x2+1+4x4+1+...+2nx2n+1(ithink)S=nn=02nx2n+1total(n+1)termsS1x1=(1x+11x1)+2x2+1+4x4+1+..+2nx2n+1S1x1=(2x21+2x2+1)+4x4+1+..+2nx2n+1s1x1=(4x41+4x4+1)+..+(2nx2n+1)S1x1=(8x81)+...+(2nx2n+1)...........S1x1=(2n+1x2n+11)S=1x12n+1x2n+11

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