Question

macalurins series of x/ e^x -1​

Answer 1

Answer:

I was solving Taylor series problems for my calculus class and was stuck with this concept.

Suppose a function,

f(x,y)=xey

f(x,y)=xey

And we know that for f(y)=eyf(y)=ey, the Maclaurin series exists as

ey=∑n=0∞ynn!

ey=∑n=0∞ynn!

Then, can I simply multiply xx to the series above such that:

f(x,y)=x⋅∑n=0∞ynn!

f(x,y)=x⋅∑n=0∞ynn!

Because xx is not varied by any nn terms, is it possible to just multiply it?

I'm greatly confused and would appreciate your help.

Thanks,