The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is

If $x>\sqrt{3}$ and $\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}$ is expanded in terms of powers of $x$, then the coefficient of $x^{-8}$ is

$$ \sum\limits_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)= $$

For all $n \in N, \frac{3^n-1}{2} \geq$