Write the following power series as a function

e) $\sum_{n=0}^{\infty}\frac{2^{n}x^{3n}}{n!}$

Question

Write the following power series as a function

e)  $\sum_{n=0}^{\infty}\frac{2^{n}x^{3n}}{n!}$

kinggeorge · Answer

Just for easier reading: $$\Large \sum_{n=0}^{\infty}\frac{2^{n}x^{3n}}{n!}$$

anonymous · Answer

ok..

kinggeorge · Answer

This isn't actually my best area of expertise unfortunately. Perhaps @joemath314159 help out with this?

anonymous · Answer

ok any help would be apreciated

anonymous · Answer

isnt it:$$\frac{2^nx^{3n}}{n!}=\frac{(2x^3)^n}{n!}$$So that summation is really just$$e^{2x^3}$$?

anonymous · Answer

mm, that i really dont know..maybe George can answer..

kinggeorge · Answer

I think that's right.

anonymous · Answer

Im using the fact that:$$e^x=\sum_{n=0}^\infty \frac{x^n}{n!}$$in place of x we have 2x^3 though.

anonymous · Answer

ok is this end solution, or is there  someting needed to be add?

anonymous · Answer

That should be it.  they wanted you to write that power series as a function, and it turned out to be e^(2x^3). Done and done :)

anonymous · Answer

ok thank you very much both of you :) i am happy that i found this website and you guys