GATE | GATE-CS-2005 | Question 50

Let G(x) = 1/(1 – x)2 = GATECS2005Q50, where | x | < 1. What is g(i) ?
(A) i
(B) i+1
(C) 2i
(D) 2i


Answer: (B)

Explanation: B is the correct option. Let us put values


S = 1 + 2x + 3x2 + 4x3 + ..........
Sx =    x  + 2x2 + 3x3 + ..........  
S - Sx = 1 + x + x2 + x3 + ....
S - Sx = 1/(1 - x) [sum of infinite GP series with ratio < 1 is a/(1-r)]
S = 1/(1 - x)2 


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