Convergence of series

[Dirtyheads]

Hi,

I am actually studying for my calculus 2 class.

I try to understand how to find the convergence of geometric series, but i have a lot of difficulty to figure out what is my "r" variable.

Let say i have the problem : 1/(4n² -1). N starts at 1 and goes to infinity. I did the first 5 variables of that serie. So i know my that my a = 1/3 and i know that i have to end with this formula :a*r^n-1, i just dont know how to get there.

Thanks for your help

 

[pka]

I try to understand how to find the convergence of geometric series, but i have a lot of difficulty to figure out what is my "r" variable.
Let say i have the problem : 1/(4n² -1). N starts at 1 and goes to infinity. I did the first 5 variables of that serie. So i know my that my a = 1/3 and i know that i have to end with this formula :a*r^n-1, i just dont know how to get there.

You seem to have a gross misunderstanding of geometric series.
\(\displaystyle \displaystyle\sum\limits_{n = 1}^\infty {\dfrac{1}{{4{n^2} - 1}}} \) is not geometric.

That series does converge. Use partial fractions to rewrite it. Then use collapsing sums to find the sum.

 

[Dirtyheads]

You seem to have a gross misunderstanding of geometric series.
\(\displaystyle \displaystyle\sum\limits_{n = 1}^\infty {\dfrac{1}{{4{n^2} - 1}}} \) is not geometric.

That series does converge. Use partial fractions to rewrite it. Then use collapsing sums to find the sum.

Cool thanks i think i found the answer!