sum of series convergence or divergence?

**Jessica11** · October 29th 2009, 11:28 AM

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

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

**Plato** · October 29th 2009, 12:19 PM

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.

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

**redsoxfan325** · October 29th 2009, 02:16 PM

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.

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.

**Danny** · October 29th 2009, 02:21 PM

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.

**redsoxfan325** · October 29th 2009, 03:09 PM

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.

**Danny** · October 29th 2009, 03:28 PM

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.

**Plato** · October 29th 2009, 03:33 PM

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.

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.

**Danny** · October 29th 2009, 03:47 PM

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.

**Jessica11** · October 29th 2009, 06:17 PM

so if it is convergent then how do I find the sum of it?

**Danny** · October 29th 2009, 07:02 PM

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.

**Jessica11** · October 29th 2009, 08:34 PM

thank you!

Thread: sum of series convergence or divergence?

LinkBack

Thread Tools

Display

sum of series convergence or divergence?

Similar Math Help Forum Discussions

Series convergence/divergence

Convergence, Divergence of a series

series convergence and divergence

Convergence/Divergence of a series

Series(convergence divergence)

Search Tags