Question

By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series.

A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...=

B) 1-(2^2)/(2!)+(2^4)/(4!)-(2^6)/(6!)+...+((-1)^(k)2^(2k))/((2k)!) +...=

Answer 1

e^x = 1+x+x^2/2! + ...
Looks like the series is e^5

Since cos(x) = 1 - x^2/2! + ...
Looks like the series is cos(2)