## anonymous 5 years ago how do you find the Geometric sum of 24+12+6+3 . . .

1. anonymous

If a and b are positive integers such that ab = 125, then (a-b)^(a+b-4) is equal to ?

2. anonymous

I don't know what that means haha im super confused

3. anonymous

Rule of the sum:$24*\sum_{0}^{\infty} 1/2^n$ Nifty trick for geometric series with initial number a and ratio r:$24*\sum_{0}^{\infty} 1/2^n = a/(1-r) = 24/(1-1/2) = 48$

4. anonymous

well you got the right answer. i just don't understand it

5. anonymous

The trick is: $a*\sum_{0}^{\infty}(r)^n = a/(1-r)$ As long as -1 < r < 1

6. anonymous

i used S = t1 / 1-r

7. anonymous

but i got 12

8. anonymous

That's the same thing :D

9. anonymous

then how did I get 12? hahaha

10. anonymous

You multiplied by 1/2 instead of divided 24/(1/2) = 48, not 12

11. anonymous

OHHHHH

12. anonymous

wow that was embarassing hahaha

13. anonymous

thanks daniel :)

14. anonymous

No it isn't. I do that all the time :D

15. anonymous

No worries :D

16. anonymous

i actually need a lot more help

17. anonymous

if youve got some extra time :D

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