Ans. (40.00)
Sol. $\lim\limits_{x\to1}{x+x^2+x^3+.....+x^n-n\over x-1}=820\left({0\over0}\right)$
$\lim\limits_{x\to1}{x+2x+3x^2+.....+nx^{n-1}\over1}=820$
$\implies1+2+3+.....+n=820$
$\implies{n(n+1)\over2}=820$
$\implies n^2+n=1640$
$\implies n^2+n-1640=0$
$\implies n=40\quad\quad n\in N$