I need help solving this task, if anyone had a similar problem it would help me.
The task is: Prove
$$\sum_{k=0}^{n} {n+1\choose k+1}=2^{n+1}-1.$$
It is not clear to me why this $-1$ occurs.
Thanks in advance!
2026-04-06 05:17:28.1775452648
Binomial coefficients prove $\sum_{k=0}^{n} {n+1\choose k+1}=2^{n+1}-1 $
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For a combinatorial proof, count the nonempty subsets of $\{1,2,\dots,n+1\}$ in two ways. The RHS takes all subsets and subtracts $1$ for the empty set. The LHS conditions on the cardinality $k+1$ of the subset.