sum of series convergence or divergence?

• Oct 29th 2009, 12:28 PM
Jessica11
sum of series convergence or divergence?
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.
http://www.webassign.net/cgi-bin/sym...2F%2820%5En%29

i thought it was 0..that's wrong help please?

• Oct 29th 2009, 01:19 PM
Plato
Quote:

Originally Posted by Jessica11
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.

$\sum\limits_{n = 1}^\infty {\frac{{5^n + 4^n }}
{{20^n }}} = \sum\limits_{n = 1}^\infty {\frac{1}
{{4^n }}} + \sum\limits_{n = 1}^\infty {\frac{1}
{{5^n }}}$
• Oct 29th 2009, 03:16 PM
redsoxfan325
Quote:

Originally Posted by Jessica11
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.
http://www.webassign.net/cgi-bin/sym...2F%2820%5En%29

i thought it was 0..that's wrong help please?

The terms of the series go to zero (that's one of the conditions for convergence), but their sum does not.
• Oct 29th 2009, 03:21 PM
Jester
Quote:

Originally Posted by redsoxfan325
The terms of the series go to zero (that's one of the conditions for convergence), but their sum does not.

That's not necessarily true. The terms going to zero says nothing of the convergence or divergence of a series.
• Oct 29th 2009, 04:09 PM
redsoxfan325
Quote:

Originally Posted by Danny
That's not necessarily true. The terms going to zero says nothing of the convergence or divergence of a series.

I said that's one of the conditions. The terms have to go to zero for the series to converge, but obviously it alone doesn't imply convergence.
• Oct 29th 2009, 04:28 PM
Jester
Quote:

Originally Posted by redsoxfan325
I said that's one of the conditions. The terms have to go to zero for the series to converge, but obviously it alone doesn't imply convergence.

I simply don't want people to think that the terms going to zero implies convergence! It was the way it was stated - those that don't know might find the implication.
• Oct 29th 2009, 04:33 PM
Plato
Quote:

Originally Posted by Jessica11
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.
http://www.webassign.net/cgi-bin/sym...2F%2820%5En%29 i thought it was 0..that's wrong help please?

@ Danny & redsoxfan325
What are you both talking about?
There is nothing in that post about terms of the series converging to zero.
The OP did think that the sum of the series is zero.
• Oct 29th 2009, 04:47 PM
Jester
Quote:

Originally Posted by Plato
@ Danny & redsoxfan325
What are you both talking about?
There is nothing in that post about terms of the series converging to zero.
The OP did think that the sum of the series is zero.

My comment was not to the OP but for those reading this thread. I often see that student's think that terms going to zero imply convergence. I just wanted to re-iterate that that is not necessarily true - that's all.
• Oct 29th 2009, 07:17 PM
Jessica11
so if it is convergent then how do I find the sum of it?
• Oct 29th 2009, 08:02 PM
Jester
Quote:

Originally Posted by Plato
$\sum\limits_{n = 1}^\infty {\frac{{5^n + 4^n }}
{{20^n }}} = \sum\limits_{n = 1}^\infty {\frac{1}
{{4^n }}} + \sum\limits_{n = 1}^\infty {\frac{1}
{{5^n }}}$

Each is a geometric series that converges. Treat each separately, find the sum, the add.
• Oct 29th 2009, 09:34 PM
Jessica11
thank you!