Let (1 + x)(1 + x + x^2)(1 + x + x^2 + x^3),, | vedclass

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Question

put $x=1$

$(31) !=a_{0}+a_{1}+a_{2}+\ldots \ldots$ $(1)$

put $x=-1$

$0=a_{0}-a_{1}+a_{2}-\ldots \ldots \ldots$ $(2)$

$(1)+(2) \Rightarrow

Vedclass · Accepted Answer

$\frac{(31)!}{2}$

Vedclass · Answer

put $x=1$

$(31) !=a_{0}+a_{1}+a_{2}+\ldots \ldots$ $(1)$

put $x=-1$

$0=a_{0}-a_{1}+a_{2}-\ldots \ldots \ldots$ $(2)$

$(1)+(2) \Rightarrow \frac{(31) !}{2}=a_{0}+a_{2}+a_{4}+\ldots \ldots .$

Let $(1 + x)(1 + x + x^2)(1 + x + x^2 + x^3)\,\, ......\,\,$$(1 + x + x^2 + ..... + x^{30}) = $$a_0 + a_1x + a_2x^2$ .....$+$ $a_{465}x^{465}$, then sum of $a_0 + a_2 + a_4 + ......... +$ is

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