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If  A and B are the coefficient of  x^n  in the expansions of  (1+x)^{2 n}and  (1+x)^{2 n-1} respectively, then

 

Option: 1

A = B


Option: 2

A = 2 B


Option: 3

2 A = B


Option: 4

None of these


Answers (1)

best_answer

A= coefficient of  x^n in  (1+x)^{2 n}={ }^{2 n} C_n=\frac{(2 n) !}{n ! n !}=\frac{2 \cdot(2 n-1) !}{(n-1) ! n !} \,\,....(i)

B= coefficient of   x^n  in  (1+x)^{2 n-1}={ }^{2 n-1} C_n=\frac{(2 n-1) !}{n !(n-1) !}\,\,...(ii)

By (i) and (ii) we get, A=2 B

Posted by

Ritika Jonwal

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