What is \sum_{n=0}^\infty \frac{2n^7 + n^6 + n^5 + 2n^2}{n!}

Willie Kelley

Willie Kelley

Answered question

2022-04-19

What is
n=02n7+n6+n5+2n2n!

Answer & Explanation

ze2m1ingkdvu

ze2m1ingkdvu

Beginner2022-04-20Added 16 answers

You have that if:
A(z)=n0anzn
then:
zddzA(z)=n0nanzn
In general, using D for the differentiation operator, and p a polyomial:
n0p(n)anzn=p(zD)A(z)
So you are looking for:
(2(zD)7+(zD)6+(zD)5+2(zD)2)ez
at z=1

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