$1+2+3+...+n = n(n+1)/2$ but how did somebody discover this?
2675
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
64581
How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
111805
If $a_{1}=1$ and $a_{n+1}=1+\frac{n}{a_{n}}$, then $a_{n}=\sqrt{n}+\frac{1}{2}-\frac{1}{8\sqrt{n}}+o\left(\frac{1}{\sqrt{n}}\right)$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
41645
Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
112948
Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$
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 $3k/2$
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
114212
How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
144779
The number of ways to represent $(n^2+n)/4$ as a sum of $n/2$ distinct integers in $1,\dots,n$