# Coeff. of $x^{50}$ in $(1+x)^{1000}$ + $x(1+x)^{999}$ + $x^2(1+x)^{998}$ + .... + $x^{1000}$ is

$\begin{array}{1 1} ^{1000} C_50 \\ ^{1001}C_{50} \\ ^{1001}C_{51} \\ ^{1000}C_{51} \end{array}$

$(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+......x^{1000}$ is a G.P.
$\therefore$ Sum of $1000$ terms of this G.P. is