Please leave your answer in sigma notation, and give the interval of convergence.

Question

Find the Taylor series for the following functions. You do not need to use the definition, i.e., feel free to use any known series as a template for your answer. Please leave your answer in sigma notation, and give the interval of convergence.

a) e^(-2x)

b) 3/(1+2x)

Answer 1

∑(-2x)^k/k! for k = 0 to ∞ this one comes directly from the Taylor series for e^x .... converges for all real x

3∑(-2x)^k for k=0 to ∞ this one is obtained by long division ..... converges for |x|<1