Let $A = \sum_{i=1}^{10} \sum_{j=1}^{10} \min \{i, j\}$ and $B = \sum_{i=1}^{10} \sum_{j=1}^{10} \max \{i, j\}$. Then $A + B$ is equal to

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

If $[x]$ denotes the greatest integer less than or equal to $x$,then $\sum_{n=8}^{100} \left[ \frac{(-1)^{n} n}{2} \right]$ is equal to:

Find the sum to $n$ terms of the series whose $n^{th}$ term is given by $(2n-1)^2$.

Let $75 \ldots 57$ denote the $(r+2)$ digit number where the first and the last digits are $7$ and the remaining $r$ digits are $5$. Consider the sum $S = 77 + 757 + 7557 + \ldots + 75 \ldots 57$ (where the last term has $98$ digits). If $S = \frac{75 \ldots 57 + m}{n}$,where $m$ and $n$ are natural numbers less than $3000$,then the value of $m + n$ is:

The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$ up to $8$ terms, is: