check my answer for this infinite geometric series:
1/3 - 1/9 + 1/27 - 1/81 ...
I got 1/4

Question

anonymous · Answer

20/81

lucaz · Answer

how did you get this?

anonymous · Answer

1/3 = 3/9
3/9 - 1/9 = 2/9
2/9 = 6/27
6/27 + 1/27 = 7/27
7/27 = 21/81
21/81 - 1/81 = 20/81
20/81

lucaz · Answer

it's an infinite series

raden · Answer

use this formula :
S = a/(1 - r)
here a = 1/3, r = -1/3

hartnn · Answer

yes,
1/3 / (1- (-1/3))
= 1/4 is correct

lucaz · Answer

ok, I did used that formula, wanted to ckeck.. thanks

raden · Answer

or if you want playing with algebra, it would be like this :
let p = 1/3 - 1/9 + 1/27 - 1/81 + ...
so,
p = 1/3 - 1/3(1/3 - 1/9 + 1/27 + ...)
p = 1/3 - 1/3p
p + 1/3 p = 1/3
4/3 p = 1/3
p = 1/4


welcome :)

lucaz · Answer

cool, I didn't know this method, thank you!

raden · Answer

you're welcome

hartnn · Answer

thats also how that a/(1-r) standard formula was derived :)

lucaz · Answer

I've seen a different derivation, now I prefer this one