Friday

January 30, 2015

January 30, 2015

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

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

- calculus -
**MathMate**, Tuesday, September 7, 2010 at 10:08pmIt 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 10:27pmOh, right . I forgot all about the -1. Thanks.

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

**Answer this Question**

**Related Questions**

Calculus - Determine whether the series is convergent or divergent. If it is ...

Calculus - Determine whether the series is convergent or divergent. If it is ...

calculus - determine if the series is absolutely convergent and convergent. the ...

calculus - determine if the series is absolutely convergent and convergent. the ...

calculus - for each series determine if the series is absolutely convergent and...

calculus - Determine whether the series is convergent o divergent and say what ...

calculus - is the sum from k=1 to infinity of 1/(k^2+1) convergent? i said it ...

calculus - for each series determine if the series is absolutely convergent and ...

calculus - determine if the series is absolutely convergent and convergent the ...

calculus - determine whether the series is convergent if so find sum: the sum of...