$$4 \sum _{k=0}^{\infty } \frac{(-1)^k}{2 k+1}$$

Question

anonymous · Answer

anyone know what this represent????

anonymous · Answer

should need to use the ratio test to see if this series converges or diverges

anonymous · Answer

is that all you needed to know or did i misunderstand what you were asking?

anonymous · Answer

I know what it converges to , I want to know how to get there

anonymous · Answer

alright lemme work it out and see

anonymous · Answer

you get -1/2?

anonymous · Answer

That just tell us , it converges; not what it converges to

anonymous · Answer

This series actually converge to $$\pi$$

anonymous · Answer

right...when r < 1...the series will converge

anonymous · Answer

to know what it actually converges to is miles above my head...i'm only in calc 3

anonymous · Answer

mine too, but just want to know if anyone can do it here

anonymous · Answer

yea i wouldn't even know where to start lol

anonymous · Answer

I asked about this the other day.....

anonymous · Answer

phi · Answer

It's the series representation of 4 * inverse tangent evaluated at x=1 
which gives 4*pi/4 = pi

zarkon · Answer

the ratio test here is useless.  the alternating series test is the way to go.

anonymous · Answer

wouldn't we be taking absolute value and then applying ratio test to test for absolute convergence?

zarkon · Answer

it is not absolutely convergent