Alternating Series Test - No B_n?

[FallingMan]

Homework Statement

Ʃ(-1/2)^k from 0 to infinity.

Homework Equations

Ʃ(-1)^k*B_n from 0 to infinity

where if the series converges

1. lim of B_n as n goes to infinity must = 0
2. B_n must be decreasing

The Attempt at a Solution

It doesn't look like there is a B_n in the original equation at all. Do I manipulate it algebraically somehow to extract the B_n, or is there some clever trick?

Is the B_n simply 1? If if that's the case, lim of 1 as n goes to infinity would just be one, but apparently that's not true from checking the answer (which is it does, indeed, converge).

Thanks.

 

[HallsofIvy]

There quite obviously is a B_n.

Your series is \sum (-1)^n(1/2)^n.

 

[FallingMan]

There quite obviously is a B_n.

Your series is \sum (-1)^n(1/2)^n.

I had to wrestle with my instinct that told me I'm not allowed to do that.. I guess I stand corrected.

Thanks a lot, HallsofIvy.