The sum of the $n$ smallest odd numbers is equal to $n^2$
42831
How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
137175
Fermat's little theorem proof by Euler
151375
There are $3$ Zero-Sum Numbers!
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
92106
Prove that $n$ is a sum of two squares?
18402
Sum of the reciprocals of divisors of a perfect number is $2$?
54604
Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
52241
Calculate sum of series $\sum \frac{n^2}{n!}$
143271
Finite sum of reciprocal odd integers
118571
Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?
6165
Proof by Induction $n^2+n$ is even
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
94389
Proving formula for product of first n odd numbers
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$