Prove alternating sum of binomial coefficients squared by induction
31970
Alternating sum of squares of binomial coefficients
10875
proof of binomial identity involving double sum
17551
Truncated alternating binomial sum
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
439
Alternating binomial sum with intervals of two
71564
Combinatorial proof of identity involving central binomial coefficients
107810
Induction with Binomial Coefficients
154280
Show this equality (The factorial as an alternate sum with binomial coefficients).
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
139426
Proving $ \binom n 0 ^2 + \binom n 1 ^2 + \dots + \binom n n ^2 = \binom { 2n} n $ without induction
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
131771
Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
121279
Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$