Asked by tom

Does the series converge or diverge? If it converges, what is the sum? Show your work.

∑∞n=1−4(−12)n−1
Answered by oobleck
if you don't have any fractions, there's no way it will converge
maybe you have some exponents? Use ^ if so
and also parentheses

what you have, as written, is just some multiple of n
Also, if you want to sum from 1 to ∞, maybe something like ∑(1..∞)

In other words, write something that makes sense.
Answered by tom
the fraction is -1/2
Answered by oobleck
well,
∞
∑ (-1/2)^n = -1/3
n=1

because it's just a geometric series with
a = -1/2
r = -1/2

I know that's not exactly what you have, but it should not be hard to adapt it.
Answered by Battle Angel
That didn’t help at all. What is the answer with complex a explanation?
Answered by Battle Angel
A complex*
Answered by lucky bag
frist you have to find the frist term and the common ratio by sub
how? well my submitting 1 for n in
-4x(-1/2)^n-1
this will give me a1=-4x(-1/2)1-1
then identify the common ratio
r=-1/2
simplify the expression
a1=-4
r=-1/2
substituting -4nfor a1 and -1/2 for r into this formula
s=a1/1-r
s=-4/1-(-1/2)
simplify it and this gavew me
s=- 8/3

I think these series is converge because of how we trie to simplify them together and we used a formula that gave us a sum.this expression has a limit
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