find the sum of infinit series 1 2 +2 2 x+3 2 x 2 +4 2 x 3 +.................

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PRAJVAL98 · Answer

let its sum be S. S=1+2 2 x+3 2 x 2 ….n 2 x n-1 =1+4x+9x 2 ….…...n 2 x n-1 xS=x+4x 2 +9x 3 ….(n-1) 2 x n-1 +n 2 x n S(1-x)=1+3x+5x 2 +7x 3 ….-n 2 x n use AGP formula to simplify it LET THE TERM U GET AFTER SIMPLIFYING IT BE= $ S=($-n 2 x n )/(1-x)

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find the sum of infinit series 1 2 +2 2 x+3 2 x 2 +4 2 x 3 +.................

find the sum of infinit series 1²+2²x+3²x²+4²x³+.................

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find the sum of infinit series 1 2 +2 2 x+3 2 x 2 +4 2 x 3 +.................

find the sum of infinit series 12+22x+32x2+42x3+.................

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find the sum of infinit series 1²+2²x+3²x²+4²x³+.................