Finding coefficient of $x^k$ in summation of binomial series

Question

I am not able to solve this problem

Find the coefficient of $x^k\;\;(k$ is greater than or equal to zero and lesser than or equal to $n$) in the expansion of $E = 1 + (1+x) + (1+x)^2 .... + (1+x)^n$

The final simplified answer is $(n+1)C(k+1)$

Any help would be thoroughly appreciated

voldemort · Accepted Answer · 2014-01-25T05:07:42.093

4

Since $E$ is just the sum of the geometric series, $E=\dfrac{(1+x)^{n+1}-1}{x}$ and thus the coefficient of $x^k$ is ${n+1 \choose k+1}$

edited Jan 25 '14 at 05:07

answered Jan 25 '14 at 04:47

voldemort

13,182

I am afraid I didn't understand your last step, sir. Can u pls elucidate? – user34304 Jan 25 '14 at 04:50
user34304: sure- let me edit my answer @AndréNicolas: Thanks- will edit it. – voldemort Jan 25 '14 at 05:05
Nice answer, sir. – user34304 Jan 25 '14 at 05:23

Finding coefficient of $x^k$ in summation of binomial series

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