My textbooks wants me to prove this identity in order to proceed into further questions related to this identity but I tried several hours to prove this but i failed can somebody assist me?
$$\sum_{i=0}^{n} {2n+1 \choose 2i} = 2^{2n}$$
2026-04-08 15:41:23.1775662883
Combination Identity Question
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Okay. Here are two VERY useful hints!
$\displaystyle \sum_{i=0}^n\binom{n}{i}=2^n$.
Also, $\displaystyle \binom{n}{i} = \binom{n}{n-i}$.
Also, I believe the right hand side should be $2^{2n}$.