Calculate the partial sum sn of the series calculate the

Question

Consider the serie _n=1Σ^∞ e^-2n

a. Determine the type sequence is _n=1{a_n}^∞ where a_n is the n^th terms of the given above series.

b. Calculate the partial sum S_n of the series.

c. Calculate the limit of the partial sum lim_n→∞S_n, then conclude about the convergence of the series.