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

If $2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots$ to $n$ terms $=a n^3+b n^2+c n+d$, then $a-b+c-d=$