4. Find the coefficient of x^n in the expansion of
(1+x/1!+x^2/2!+ ...........x^n/n!)^2
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1 Answers
62(1+x/1!+x^2/2!+ ...........x^n/n!)^2
now my claim is that the answer will not change if i asked you to add more terms of power greater than x^n
like x^(n+1)
doing that will have no effect.. bcos they will not contribute anything to the coefficient of x^n (which we have to find....)
so the answer will be same as
coefficient of x^n in (1+x/1!+x^2/2!+ ...........x^n/n! .......... ..... )^2
=coefficient of x^n in (e)^2x
that is a bit simpler to find :)
