How to sum $\sum_{k=1}^{n}n^2$ WITHOUT induction?
16472
Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
137155
Sum $ \sum\limits_{k=1}^{\infty} \frac{k^2}{2^k}$
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
14399
Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
108596
Proof by induction for "sum-of"
146305
Simplify sum of factorials with mathematical induction
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
123853
Finding a formula for $1+\sum_{j=1}^n(j!)\cdot j$ using induction
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?