How do you solve this difficult calculus problem?

Question

Choose the infinite series which diverges from the four infinite series listed below. (The answer slot is above the series.) If you think that they all converge, choose the answer: "The above series all converge." If you think that at least two of the series diverge, choose the answer: "At least two of the above series diverge."


a. oo
∑ (-1)^n(n^-1/2)
n=1

b. oo
∑ (n^-1/2)
n=1

c. oo
∑ (-1)^n(n^-2)
n=1

d. oo
∑ n^-2
n=1

e. The above series all converge.

f. At least two of the above series diverge.

Answer 1

A converges by Alternating Series Test (lim[n→∞] = 0; a_n ≤ a_n-1), B diverges by p-series Test (p ≤ 1), C converges by Alternating Series Test (lim[n→∞] = 0; a_n ≤ a_n-1), and D converges by p-series Test (p > 1).

So only one of the series diverges, which doesn't seem to be an option.

Answer 2

You apply the test(s) for convergence given in your textbook prior to this practice exercise.

Answer 3

I think it's E