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  • The coefficient of  in the expression <img alt="(1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+....+x^{10}" src="http://entrancecorner.oncodecogs.com/gif.latex?%281a

The coefficient of x^{7} in the expression (1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+....+x^{10} is :
Option: 1 420
Option: 2 330
Option: 3 210
Option: 4 120
 

Answers (1)

best_answer

Binomial Theorem

(x+y)^{n}=^{n} C_{0} x^{n}+^{n} C_{1} x^{n-1} y+^{n} C_{2} x^{n-2} y^{2}+\cdots+^{n} C_{n} y^{n}\;\;where,\;n\in \mathbb{N}

 

Now,

Given series S is a GP, with a = (1+x)10 , r = x/(1+x), n = 11

So, S = \frac{(1+x)^{10} \left ( \frac{x}{1+x}^{11}-1 \right )}{(\frac{x}{1+x})-1}

= (1+x)11 - x11

Hence coefficient of x7 is 11C7 = 330

Correct option (2)

Posted by

Ritika Jonwal

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