# Math Help - calculus bc question

1. ## calculus bc question

hi, i have a set of ap practice problems to do, and theres a topic on one of these questions that we havent covered in class. could anyone help me out please?

which of the following series converge?
I.) the summation from 1 to infinity of (k)/(n^2) where k is a constant
II.) the summation from 1 to infinity of (-1)^n/(n^1/2)
III.) the summation from 1 to infinity of (0.4)^(n-1)

a.) I only
b.) II only
c.) III only
d.) I and III
e.) I, II, and III

thanks so much

2. Originally Posted by holly123
which of the following series converge?
I.) the summation from 1 to infinity of (k)/(n^2) where k is a constant
II.) the summation from 1 to infinity of (-1)^n/(n^1/2)
III.) the summation from 1 to infinity of (0.4)^(n-1)

a.) I only
b.) II only
c.) III only
d.) I and III
e.) I, II, and III
all three series converge ...

I. is a p-series, p > 1

II. is an alternating series whose nth term approaches 0
(conditionally converges ... has to be alternating in sign, otherwise it diverges)

III. is a geometric series with |r| < 1

you'll learn about all of these very soon.