What is the sum of the geometric series?
4
Σ(-2)(-3) n-1
n=1

6/5

Step-by-step explanation:

First, take the 2 out of the sigma so it's easier to deal with:

2∑(-2/3)

this is in the form: ∑ ( u ) n where | u | < 1 . That means, that ∑ u n = 1 1 − u

Our u , in this case, is − 2 3 . Simply plug into the formula.

2 ( 1/1-(-2/3) = 2 (1/5/3) = 2 (3/5) = 6/5

i think it would be 42cm