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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

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

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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. 

Posted by

Deependra Verma

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