SOLUTION: Find S(with a sideways 8 beside it) if an=27(1/3)^n, n=1,2,3,4,... I have no idea how to do this problem. Please help me.

Question 37827: Find S(with a sideways 8 beside it) if an=27(1/3)^n, n=1,2,3,4,... I have no idea how to do this problem. Please help me.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
OK...

, n=1,2,3,4,...

so putting a few values of n into this formula, we get:

etc

So we have a GP: 9, 3, 1, ....
whose common ratio is 1/3.

Now formula for "sum to infinity" is:

so,

S = 13.5

which you can begin to see if you add a few of the terms up yourself:
9+3+1+(1/3)+...
is already 13.333333

jon.

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