Find the sum of the series $5^{2} + 6^{2} + 7^{2} + \ldots + 20^{2}$.

$2^2 + 4^2 + 6^2 + \dots + (2n)^2 = \dots$

The sum of $(1^2-1+1)(1!) + (2^2-2+1)(2!) + \ldots + (n^2-n+1)(n!)$ is

What is the sum of the first $16$ terms of the series $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$?

$1+(1+3)+(1+3+5)+(1+3+5+7)+\ldots$ to $10$ terms $=$

The sum of the infinite series $(\frac{1}{3}+\frac{4}{7})+(\frac{1}{3^{2}}+\frac{1}{3}\times\frac{4}{7}+\frac{4^{2}}{7^{2}})+(\frac{1}{3^{3}}+\frac{1}{3^{2}}\times\frac{4}{7}+\frac{1}{3}\times\frac{4^{2}}{7^{2}}+\frac{4^{3}}{7^{3}}) + \dots$ is equal to -