GATE CSE
First time here? Checkout the FAQ!
x
0 votes
124 views

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

(A) i
(B) i+1
(C) 2i
(D) 2i
 

asked in Combinatory by Loyal (4.5k points)   | 124 views

1 Answer

+5 votes
Best answer
$\frac{1}{1-x} = 1 + x + x^2 + x^3 + x^4 + x^5 + \dots + \infty$

Differentiating it w.r.to $x$

$\frac{1}{(1-x)^2} = 1 + 2x + 3x^2 + 4x^3 + 5x^4 + \dots + \infty$

$\sum_{i=0}^{\infty} g(i)x^i = g(0) + g(1)x + g(2)x^2 + g(3)x^3 + \dots + \infty$

Comparing above two, we get $g(1) = 2, g(2) = 3 \color{red}{\Rightarrow g(i) = i+1}$
answered by Veteran (24.3k points)  
selected by
Top Users Feb 2017
  1. Arjun

    5278 Points

  2. Bikram

    4230 Points

  3. Habibkhan

    3942 Points

  4. Aboveallplayer

    3086 Points

  5. Debashish Deka

    2378 Points

  6. sriv_shubham

    2308 Points

  7. Smriti012

    2236 Points

  8. Arnabi

    2008 Points

  9. sh!va

    1672 Points

  10. mcjoshi

    1660 Points

Monthly Topper: Rs. 500 gift card

20,857 questions
26,009 answers
59,671 comments
22,107 users