# Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!

• Mar 29th 2013, 03:28 PM
yankees2694
Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!
Let an is the following.http://www.webassign.net/cgi-perl/sy...n)%2F(8 n%2B1)

(a) Determine whether {an} is convergent.

(b) Determine whether http://www.webassign.net/cgi-perl/sy...)^infinity a_n is convergent.

Also the answer to be is that it is not convergent, but why????????
• Mar 29th 2013, 03:41 PM
Plato
Re: Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!
Quote:

Originally Posted by yankees2694
Let an is the following.http://www.webassign.net/cgi-perl/sy...288%20n%2B1%29
(a) Determine whether {an} is convergent.
(b) Determine whether http://www.webassign.net/cgi-perl/sy...infinity%20a_n is convergent.

The part a) is convergent divide all by $\displaystyle n$.

For part b) $\displaystyle \sum\limits_{n = 1}^\infty {{a_n}}$ converges only if $\displaystyle (a_n)\to 0$.
• Mar 29th 2013, 03:41 PM
Shakarri
Re: Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!
a) Divide all parts of the fraction by the dominant term (the term that increases fastest when n increases). Then see what happens when n tends to infinity.

b) The infinite sum can only converge if an is a null sequence.

Haha Plato replied less than a minute before me.
• Mar 30th 2013, 08:38 AM
hollywood
Re: Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!
So for (b), your series diverges since the terms do not approach zero (you will show in part (a) that they approach a different number). Some textbooks call this the Divergence Test.

I hope that clarifies Plato and Shakarri's answer a little.

- Hollywood
• Mar 30th 2013, 08:53 AM
MINOANMAN
Re: Determining if An is convergent or not???!?!??!?!????????? And explain WHY!!
Yankey :

Lim(an) = 1/2 different than zero...therefore the Σan diverges...the divergent test as Holywood mentioned....