# Infinite Series ?COnverge or Diverge

1. May 20, 2010

### SAT2400

Infinite Series!!??COnverge or Diverge

1. The problem statement, all variables and given/known data
1.
∑(infinity, k=1) 5k^(-3/2)

2.
∑(infinity, k=1) 1/(k+3)
2. Relevant equations
converge or diverge

3. The attempt at a solution
1. converges p=3/2... 5/(infin)=> 0
2. diverges p=1
I still don't get why 2 diverges? 1 converges b/c it gets to 0??

2. May 20, 2010

### lanedance

Re: Infinite Series!!??COnverge or Diverge

use integral test for 1

for 2 try and find a comparison test with a harmonic series(1/k)

3. May 20, 2010

### SAT2400

Re: Infinite Series!!??COnverge or Diverge

Umm, I am not supposed to use those tests...

Is there any other method??

4. May 20, 2010

### mg0stisha

Re: Infinite Series!!??COnverge or Diverge

Can't you just use the test for divergence for #2?

EDIT: I think it works for both #1 and #2.

5. May 20, 2010

### SAT2400

Re: Infinite Series!!??COnverge or Diverge

6. May 21, 2010

### mg0stisha

Re: Infinite Series!!??COnverge or Diverge

The best that I can do is tell you what the Test for Divergence is.

The Test for Divergence states that:

If $$lim _{x\rightarrow\infty} a_{n} \neq 0, \sum a_{n} diverges.$$

P.S. My LaTeX is weak, could someone tell me how to add spaces?

7. May 21, 2010

### lanedance

Re: Infinite Series!!??COnverge or Diverge

8. May 21, 2010

### lanedance

Re: Infinite Series!!??COnverge or Diverge

i think both the terms go to zero in the limit? so it doesn't show divergence?

as for latex, just found out myself (from other posts)-, you can also add the slash to make the limit show correctly, have a look at these:
single space "\"
$$\lim _{x\rightarrow\infty} a_{n} \neq 0, \ \sum a_{n} \ diverges.$$

multispace 0.5 inches "\hspace{0.5 in}"
$$\lim _{x\rightarrow\infty} a_{n} \neq 0, \hspace{0.5 in} \sum a_{n} \ diverges.$$

using itex (inline tex) and splitting into 2 parts
$\lim _{x\rightarrow\infty} a_{n} \neq 0$, $\sum a_{n} \ diverges.$

Last edited: May 22, 2010
9. May 21, 2010

### ice109

Re: Infinite Series!!??COnverge or Diverge

what are you talking about? #1 converges and #2 does diverge but you're not going to show it using the divergence test since $lim_{k\rightarrow \infty} \frac{1}{(k+3)} = 0$

to op:

for #1 it's a p series
for #2 show that it's bigger than $$\sum \frac{1}{5k}$$ and then show that that diverges

10. May 22, 2010

### mg0stisha

Re: Infinite Series!!??COnverge or Diverge

Wow, I apologize to the OP. Guess I should stop doing math at 4 am and just go to bed! Sorry for any confusion, I definitely see my blindingly obvious mistakes now.