I have come across the following in regards to a taylor series. I know what the solution is but not how it was arrived at.
1-summation n=0->inf ((-1)^n*4^n*x^2n)/2n!
It's the 1-summation part that has me stumped.
I have no idea what "1- summation" means! Is it possible that the "1" is just the problem number? Also "x^2n" could be (x^2)n or x^(2n)- I suspect the latter- and 2n! correctly is 2(n!) but I suspect you mean (2n)!
If I am correct about what you mean then this is $\displaystyle \sum_{n=0}^\infty \frac{(-1)^n 4^n x^{2n}}{(2n)!}= \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!}(4x^2)^n= sin(4x^2)$