question_answer

If \[\left| x \right|<1\], then the coefficient of \[{{x}^{n}}\] in expansion of \[{{(1+x+{{x}^{2}}+{{x}^{3}}+....)}^{2}}\] is   AIEEE  Solved  Paper-2002

A) n                                

B)           \[n-1\]                    

C)           \[n+2\]                   

D)           \[n+1\]

Correct Answer: D

Solution :

Since, \[{{(1+x+{{x}^{2}}+{{x}^{3}}+...)}^{2}}={{[{{(1-x)}^{-1}}]}^{2}}\]                                                    . Coefficient of  in                    = Coefficient of  in                                       .