calculus - The following is a Taylor Series evaluated a particular value of x, find the sum of the series.

This is the Taylor Series in question 1 + $\frac{2}{1!}$+$\frac{4}{2!}$+$\frac{8}{3!}$+...+$\frac{2^n}{n!}$+...

I know how to find whether or not the series converges or diverges easily using the ratio test. I find that it converges. However, I don't know exactly how to find what value it converges to because the limit that you find using the ratio test doesn't yield the actual value that you converge to correct?

Answer

That is correct, the ratio test does not give a value for the series. If you want a value for the series, take a look at the power series of $e^x$