How can i solve the series n=0n3(n+1)! ?

1 Answer
Jul 27, 2018

Calling f(x)=ex1x=k=0xk(k+1)! we have

xddx(xddx(xddxf(x)))=k=0k3xk(k+1)!=ex(x3+x1)+1x

now making x=1 we have

k=0k3(k+1)!=e+1