Solving the B Sequence: Tips and Tricks for Finding the Closed-Form Solution

[mknabster]

This sequence is stumping me, how would I go about solving this?

Write the sequence B = 1, -1/2, +1/4, -1/8, +1/16, ... in closed-form. I tried using (-1) has the top with different variable son the bottom, but nothing seems to add up. The 1 in the front is throwing me off. Any help would be appreciated. thank you

 

[mathman]

(-1/2)ⁿ, where n starts from 0.

 

[mknabster]

Oh so you do include 0 in the number line. HOw does this look: 1/(-2)ⁿ

 

[mathman]

Oh so you do include 0 in the number line. HOw does this look: 1/(-2)ⁿ

It looks the same. -1/2 = 1/(-2)

Also (a/b)ⁿ = aⁿ/bⁿ