Alternating sum of binomial coefficients multiplied by (1/k+1)
76319
How to prove $\sum\limits_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$?
47052
How can I simplify this expression involving binomial coefficients?
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
105237
Alternating sum of binomial coefficients identity
51008
Evaluating a sum involving binomial coefficient in denominator
152845
Every integer is the unique sum of a "decreasing" sequence of binomial coefficients
626
Sum of combinations with varying $n$
132249
Sum of every $k$th binomial coefficient.
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero
13236
Proving equality - a sum including binomial coefficient $\sum_{k=1}^{n}k{n \choose k}2^{n-k}=n3^{n-1}$
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
144571
A conjecture including binomial coefficients
107810
Induction with Binomial Coefficients
155496
sum of combinations $\binom n{0} + \binom n{3} + \binom n{6} +... +\binom n{3k}$