If limit n->∞ Σ (from n=1 to n) of "a sub k" exists and has a finite value, the infinite series Σ (from n=1 to n) of "a sub k"

Question

a) unbounded
b) convergent
c) increasing -----> my answer. Can you check for me, pls? Thanks
d) divergent

Answer 1

nope. the terms might be negative.
But if the infinite sum exists and is finite, the partial sums converge to that value.

and if the terms are a sub k, then the sum is Σ (from k=1 to n)