How to prove the sum of triangular numbers in the form n(n+1)(n+2)/6?
108274
Sum of the first $n$ triangular numbers - induction
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
112929
How do I prove $\frac 34\geq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{n+n}$
33104
Combinatorial Proof with Summation Identity
65983
Combinatorial proof of binomial coefficient summation identity
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
137507
triangular series and inequality
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
4573
Explicitly finding the sum of $\arctan(1/(n^2+n+1))$
20548
General formula to obtain triangular-square numbers
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
50972
Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
101899
Proof By Induction of a Sum
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$