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# The coefficient of $x^m$ in the expansion 1 + $(1+x)$ + $(1+x)^2$ + ..... + $(1+x)^n$ is

$\begin{array}{1 1} ^{n+1} C_{m+1} \\ ^n C_m+1 \\ ^{n+1} C_m \\^nC_m \end{array}$

$1+(1+x)+(1+x)^2+..........(1+x)^n$ is a G.P.