Show the closed form of the sum $\sum_{i=0}^{n-1} i x^i$
7063
How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$?
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
2885
Prove that $\sum\limits_{i=1}^n 2i\binom{2n}{n-i}= n\binom{2n}{n}$
97266
Summation by parts (finite calculus) of $\sum\limits_{i=0}^{n}i\cdot a^i$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
60031
Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
9610
Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
86348
Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
119606
Closed form of summation
17332
How to compute $\sum\limits_{n=1}^{\infty}\frac{1}{x^n-1}$?
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
98941
Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
39659
Is there a closed formula for this summation?
57759
Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$