Posted by **bill** on Tuesday, September 7, 2010 at 8:10pm.

The sum from 0 to infinity of (-1)^n(3/3^n) is convergent or divergent? If convergent, what is the sum?

I got that it's convergent and the sum is 9/2, but that's wrong.

- calculus -
**MathMate**, Tuesday, September 7, 2010 at 10:08pm
It is not clear without sufficient parentheses what the expression really is.

I assume it to be:

Sum((-1)^n * (3/3^n)) for n=0 -> ∞

This is an alternating geometric series.

(9/2) is the correct sum for the geometric series (non-alternating).

Write out the first few terms of the series:

3 - 3/3 + 3/9 - 3/27 + 3/81 - ...

which can be regrouped into two geometric series:

3(1+1/9+1/81+...) - (1+1/9+1/81+...)

=3(9/8) - (9/8)

=2(9/8)

=9/4

Note that if the minus sign becomes a plus sign, we get the geometric sum of 9/2.

- calculus -
**bill**, Tuesday, September 7, 2010 at 10:27pm
Oh, right . I forgot all about the -1. Thanks.

- calculus -
**MathMate**, Tuesday, September 7, 2010 at 10:38pm
You're welcome!

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