SOLUTION: An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125,... what is the sum, S, of the infinite series?

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Question 175168: An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125,... what is the sum, S, of the infinite series?
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
The sequence that generates 1, 1/5, 1/25, 1/125,... is a%5Bn%5D=%281%2F5%29%5En. Take note that the sequence is in the form a%5Bn%5D=a%2Ar%5En where a=1 and r=1%2F5.


Remember, the formula for the sum of an infinite series is

S=a%2F%281-r%29


S=1%2F%281-1%2F5%29 Plug in a=1 and r=1%2F5


S=1%2F%284%2F5%29 Subtract


S=5%2F4 Invert the fraction and multiply


So the answer is S=5%2F4 which means that 1+1/5+1/25+1/125+...=5/4

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F5%5E%28n-1%29 n= natural numbers