∞∑n=1 -4(-1/2) n-1
I'll assume you mean
∞
∑ -4(-1/2)^(n-1)
n=1
That sum is just
-4*∑(-1/2)^(n-1)
which is a geometric progression with
a = 1
r = -1/2
and sum = 1/(1-r) = 2/3
So, your sum is just -8/3
∞
∑ -4(-1/2)^(n-1)
n=1
That sum is just
-4*∑(-1/2)^(n-1)
which is a geometric progression with
a = 1
r = -1/2
and sum = 1/(1-r) = 2/3
So, your sum is just -8/3