By recognizing each series below as a taylor series evaluated at a particular value of xx, find the sum of each convergent series

Let x=3 therefore 1+3+3^2/2!+3^3/3!+3^4/4!+⋯+3^n/n! + ... becomes: 1 + x + x^2/2! + x^3/3! + ... + x^n/n! We know that the inf SUM (n=0) x^n/n! = e^x

then you need to replace x so the answer should be e^3

Same Idea for this one let x=2 1 - x^2/2! + x^4/4! + x^6/6! + ... + [ (-1) ^n * x^ (2n) / (2k!) ]

We all know that the inf SUM (n=0) [ (-1) ^n * x^ (2n) / (2k!) ] = cos x