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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+.................

Grade:12

1 Answers

PRAJVAL98
18 Points
7 years ago
let its sum be S.
S=1+22x+32x2….n2xn-1=1+4x+9x2….…...n2xn-1
xS=x+4x2+9x3….(n-1)2xn-1+n2xn
S(1-x)=1+3x+5x2+7x3….-n2xn
 
use AGP formula to simplify it    LET THE TERM U GET AFTER SIMPLIFYING IT BE= $
 
S=($-n2xn)/(1-x)
 

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