How to change $\dfrac{k(k+1)(2k+1)}6+(k+1)^2$ into $\dfrac{(k+1)(k+2)(2k+3)}6$
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
145444
Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$
57503
How find $\sum_{k \in A} \frac{1}{k-1} $ for $ A = \{ m^n| \text{ } m, n \in Z \text { and } m, n \ge 2 \} $
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
19285
simplifying $ (h^2_2-h^2_3)\over ({1\over h_3})-({1\over h_2})$
21121
Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
124135
A general formula for $\sum (k-1)(k-2)(k-3)$?
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
14306
What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$
107179
Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
24864
$ \Big(\dfrac{x^7+y^7+z^7}{7}\Big)^2=\Big(\dfrac{x^5+y^5+z^5}{5}\Big)^2\cdot\Big(\dfrac{x^4+y^4+z^4}{2}\Big) $
60104
Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
143093
Determining k: $\int_{6}^{16} \frac{dx}{\sqrt{x^3 + 7x^2 + 8x - 16}} = \frac{\pi}{k}$
114219
The map $f:\mathbb{Z}_3 \to \mathbb{Z}_6$ given by $f(x + 3\mathbb{Z}) = x + 6\mathbb{Z}$ is not well-defined