Determine whether the following series converges or diverges.
∑ₙ₌₁[infinity]ne⁻ⁿ
a. Diverges, by the nth term test for divergence
b. Converges, by the nth term test for divergence
c. Diverges, by the alternating series test
d. Converges, by the alternating series test
e. Diverges, by the p-series test
f. Converges, by the p-series test
g. Diverges, by the integral test
h. Converges, by the integral test
i. Diverges, by the basic comparison test
j. Converges, by the basic comparison test
k. Diverges, by the limit comparison test
l. Converges, by the limit comparison test
m. Diverges, by the ratio test
n. Converges, by the ratio test
o. Diverges, by Raabe's test
p. Converges, by Raabe's test
q. Diverges, by Bertrand's test
r. Converges, bý Bertrand's test
s. Diverges, by Gauss's test
t. Converges, by Gauss's test