Question

Does the series converge or diverge? If it converges, what is the sum?

Answer 1

What is the series?

Answer 2

So looking at this series, we can see that it is a geometric Sum, and it follows the formula \[\sum_{n=1}^{\infty}ar ^{n-1}\]

Answer 3

my observing the behavior of r, \[|r|<1\] and we see that \[|-\frac{ 1 }{ 2 }|<1\] so we proved the series converges. And now in order to find the sum we apply what we know of the series : a= -4, r= (-1/2) We apply that to the formula \[\frac{ a }{ 1-r }\] and you can get your sum! :)

Answer 4

thank you so much! i understand :)

Answer 5

Woo! no problemo!!

Answer 6

Show me some looooovin! :)

Answer 7

how do i do that? :o