Series with reciprocal of binomial coefficients

Asked Mar 15 '20 at 17:22

Active Mar 15 '20 at 17:44

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I'm stuck on this problem… I have to find the sum of $$\sum_{k=0}^n \frac{(-1)^k}{\binom{n}{k}}$$ with $n$ an even natural number. The book reports the answer and that's $\frac{2n+2}{n+2}$ but I sincerely don't know where to start. Some ideas?

The problem is took by Advanced Calculus Explored, by Hamza Alsamraee.

edited Mar 15 '20 at 17:44

user729424

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asked Mar 15 '20 at 17:22

bianco

you can find an answer here https://math.stackexchange.com/questions/3251604/proving-that-sum-k-0n-frac-1kn-choose-k-1-1n-fracn1n – Z Ahmed Mar 15 '20 at 17:37
Oh, thanks a lot! I tried to found an answer before asking but i came up with nothing :( – bianco Mar 15 '20 at 18:05
Yes, this does happen, Cheers – Z Ahmed Mar 15 '20 at 18:26

Series with reciprocal of binomial coefficients

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