The coefficient of ${x^{301}}$ in $${(1 + x)^{500}} + x{(1 + x)^{499}} + {x^2}{(1 + x)^{498}}\, + \,...\, + \,{x^{500}}$$ is :
Solution
<p>The coefficient of ${x^{301}}$ in
<br/><br/>$${(1 + x)^{500}} + x{(1 + x)^{499}} + {x^2}{(1 + x)^{498}}\, + \,...\, + \,{x^{500}}$$</p>
<p>$${}^{500}{C_{301}} + {}^{499}{C_{300}} + {}^{498}{C_{299}}\, + \,...\, + \,{}^{199}{C_0}$$</p>
<p>$$ = {}^{500}{C_{199}} + {}^{499}{C_{199}} + {}^{498}{C_{199}}\, + \,...\, + \,{}^{199}{C_{199}}$$</p>
<p>$= {}^{501}{C_{200}}$</p>
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Applications of Binomial Theorem
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