SOLUTION: I am having trouble with Variation, Progression, and Theorems. My question is an infinate geometric series has 1 and 1/5 as it's first two terms: 1, 1/5, 1/25, 1/125, ........ What

Algebra ->  Absolute-value -> SOLUTION: I am having trouble with Variation, Progression, and Theorems. My question is an infinate geometric series has 1 and 1/5 as it's first two terms: 1, 1/5, 1/25, 1/125, ........ What      Log On


   

Question 6612: I am having trouble with Variation, Progression, and Theorems. My question is an infinate geometric series has 1 and 1/5 as it's first two terms: 1, 1/5, 1/25, 1/125, ........ What is the sum, S, of the infinate series?
I have tried to do this question on my own and I am not having any luck, Can you please help me?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
to have a sum to infinity for a geometric progression/series, you need to have numbers that get successively smaller, so that adding them approaches some final answer... if the numbers got bigger, then the summation would always be increasing.

So, that is why the one stipulation is |r|<1 ie -1
Formula: S%5Binf%5D+=+a%2F%281-r%29, so:

Sum = 1%2F%281-%281%2F5%29%29
Sum = 1%2F%284%2F5%29
Sum = 5%2F4
Sum = 1.25

jon.