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The coefficient of x^8 in the expansion of (1+x^2/2!+x^4/4!+x^6/6!+x^8/8!)^2 is

Answers (1)

D Deependra Verma

Solution: We have ,

$(1+fracx^22!+fracx^44!+fracx^66!+fracx^88!)^2$

The coefficient of $x^8$ is

$frac10!8!+frac12!6!+frac14!4!+frac18!0!$

$frac10!8!+frac12!6!+frac14!4!+frac18!0!=frac18![c_0+c_2+c_4+c_6+c_8]$

$Rightarrow$ $frac18![c_0+c_2+c_4+c_6+c_8]=frac2^78!=frac1315.$

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