Finding a closed-form for the sequence 1, -1/2, 1/4, -1/8, 1/16

mknabster · Sep 26, 2011

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 · Sep 26, 2011

(-1/2)ⁿ, where n starts from 0.

mknabster · Sep 26, 2011

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

mathman · Sep 27, 2011

mknabster said:

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

Finding a closed-form for the sequence 1, -1/2, 1/4, -1/8, 1/16

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