# Series and sequence help

1. Nov 21, 2005

### JessicaSTAR

hi everyone, im having trouble with a few problems, i was wondering if anyone can help me thank.
1.) given r= 11/22

a.)consider the sequence {nr^r}. if convergent find limit. if divergent find if it goes to inf or minus inf. or div otherwise
lim nr^r = ?
n->infinity

b.)take my word for it that it can be shown that
sigma i=1 to n ir^i = (n(r^(n+2))-(n+1)(r^(n+1))+r)/((1-r)^2)

now consider the series sigma n=1 to infinity nr^r
sigma n=1 to infinity nr^r = ?

2.) An= 8n/(6n+13)
the series sigma n=1 to infinity (An) =?
if convergent, find sum. if divergent find it it goes to positive or negitive.

and 3.) An= 50/(5^n)
find whether {An} is convergent, if so, find limit.

any help would be great. thanks.

2. Nov 22, 2005

### siddharth

You mean r=0.5?
If r=0.5, then what's $$\lim_{n\rightarrow \infty} n \sqrt{0.5}$$
You have lost me here. If r=0.5, how is the series convergent in the first place?
What does the divergence test tell you?
You have already stated how to find if a sequence is convergent or divergent. Why not apply it here?

Last edited: Nov 22, 2005
3. Nov 22, 2005

### JessicaSTAR

sorry for the first one a.) and b.) instead or nr^r i meant nr^n

ok for 2.) i got infinity

and 3.) would go to minus infinity so would it be divergent?

Last edited: Nov 22, 2005
4. Nov 22, 2005

### JessicaSTAR

i still need help on 1a and b and 3, anyhelp would be good, thanks.