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If $a_k$ is the coefficient of $x^k$ in the expansion of $(1+x+x^2)^n$ for $k=0,1,2.......,2n$ then $a_1+2a_2+3a_3+.....+2na_{2n}$ is equal to

\[\begin {array} {1 1} (a)\;-a_0 & \quad (b)\;3^n \\ (c)\;n.3^{n+1} & \quad (d)\;n.3^n \end {array}\]
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$(d)\;n.3^n $
answered Nov 7, 2013 by pady_1

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