SOLUTION: What is the sum of the infinite series whose nth term is: (7^(n-1)) / (10^n)

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Question 1191493: What is the sum of the infinite series whose nth term is:
(7^(n-1)) / (10^n)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Plugging in n=1, 2, 3... shows the first few terms to be

1/10, 7/100, 49/1000, ...

This is an infinite geometric sequence with first term 1/10 and common ratio 7/10.

The sum of an infinite geometric sequence with first term a and common ratio r is

a%2F%281-r%29

For this example, the sum is

%281%2F10%29%2F%281-7%2F10%29+=+%281%2F10%29%2F%283%2F10%29+=+1%2F3

ANSWER: 1/3