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 (nonalternating).
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!
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 2 (Series  Convergent or Divergent?)  Can someone show me a step by ...
 calculus  for each series determine if the series is absolutely convergent and ...
 calculus  determine if the series is absolutely convergent and convergent the ...
More Related Questions