If `|x| lt 1`, then find the sum of the serires ` 2+ 4x + 6x^(2) + 8x^ – InterviewSolution

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1.	If `\|x\| lt 1`, then find the sum of the serires ` 2+ 4x + 6x^(2) + 8x^(3) + ……..`.
Answer» Let `S= 2+ 4x + 6x^(2) + 8x^(3)+ … " "` (1) `x S = 2x + 4x^(2)+ 6x^(3)+…" " `(2) Eq. (1) - Eq. (2) gives `S(1-x) = 2+ 2x + 2x^(3)+ 2x^(3)+ …` `" " = 2(1+x+x^(2) + …)` `1+ x + x^(2) +... ` is an infinite GP with `a = 1, r =x and \|r\| = \|x\| lt 1` `therefore ` Sum of the series = `(1)/(1-x)` `therefore S = (2)/((1-x)^(2))` .

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