Deriving formula for sum n(n+1)
86900
Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
106280
Integrating the formula for the sum of the first $n$ natural numbers
83229
Nested summations and their relation to binomial coefficients
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
99003
How do we calculate this sum $\sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdots(n+p)}$?
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
152588
Expression for $n+n(n-1)+n(n-1)(n-2)+...+n!$
7073
How to get to the formula for the sum of squares of first n numbers?
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
9610
Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
89175
Proof of $(a+b)^{n+1}$
61547
Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
140843
How does one [easily] calculate $\sum\limits_{n=1}^\infty\frac{\mathrm{pop}(n)}{n(n+1)}$?