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Differential Calculus

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8 Sep 2007 20:44:28 IST

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Use calculus to find the sum of [1/(x+1) +2/(x^2+1) +4/(x^4+1) +.......+2^n/(x^2n+1)]

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Use calculus to find the sum of [1/(x+1) +2/(x^2+1) +4/(x^4+1) +.......+2^n/(x^2n+1)]

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venkat v.t

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Joined: 7 Aug 2007

Posts: 244

9 Sep 2007 12:47:54 IST

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Answer is 1/x+1.(providing with condition Modx is less than 1)

Sol) Consider,

(1-x)(1+x)(1+x²)(1+x⁴)....(1+x²ⁿ)=(1-x⁴ⁿ)

As n tends to infinity

(1-x)(1+x)(1+x²)(1+x⁴)(1+x⁸).....infinity =1 (x⁴ⁿtends to 0 as n tends to infinity)

Taking log on both sides to the base 'e' and differentiate on

both sides.U will get the answer.

i.e 1/x+1 + 2x/1+x² +4x³/1+x⁴+.....=1/1-x.

Hope u got it.

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