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Question Number 55914 by peter frank last updated on 06/Mar/19

	Answered by tanmay.chaudhury50@gmail.com last updated on 06/Mar/19

	$(k - 1) ∣ \frac{x^{k + 1}}{k + 1} ∣_{0}^{4} = \frac{1}{4}$ $(k - 1) (\frac{4^{k + 1}}{k + 1}) = \frac{1}{4}$ $4^{k + 2} = \frac{k + 1}{k - 1} = \frac{1 + \frac{1}{k}}{1 - \frac{1}{k}}$ $w a i t . . .$ $1) l e t k = + v e i n t e g e r t h e n l e f t h a n d s i d e i n t h e$ $f o r m o f 4^{n} b u t r i g h t h a n d s i d e i n \frac{p}{q} f o r m$ $s o k \neq + v e i n t e g e r$ $2) l e t k = - v e i n t e g e r t h e n L H S = \frac{1}{4^{n}}$ $R H S = \frac{1}{(\frac{k - 1}{k + 1})} t h a t i m p l y (\frac{k - 1}{k + 1}) i s d i v i s b l e b y 4$ $w a i t . . .$
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