Infinite Series ?COnverge or Diverge

[SAT2400]

Infinite Series!??COnverge or Diverge

Homework Statement

1.
∑(infinity, k=1) 5k^(-3/2)

2.
∑(infinity, k=1) 1/(k+3)

Homework Equations

converge or diverge

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??

 

[lanedance]

use integral test for 1

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

 

[SAT2400]

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

Is there any other method??

 

[mg0stisha]

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

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

 

[SAT2400]

could you please show me?thanks

 

[mg0stisha]

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

The Test for Divergence states that:

If [tex] lim _{x\rightarrow\infty} a_{n} \neq 0, \sum a_{n} diverges. [/tex]

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

 

[lanedance]

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

Is there any other method??

what can you use? i can't read your question/notes/teachers mind ;)

 

[lanedance]

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

The Test for Divergence states that:

If [tex] lim _{x\rightarrow\infty} a_{n} \neq 0, \sum a_{n} diverges. [/tex]

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

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

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 "\"
[tex] \lim _{x\rightarrow\infty} a_{n} \neq 0, \ \sum a_{n} \ diverges. [/tex]

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

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

 

[ice109]

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

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

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

to op:

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

 

[mg0stisha]

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.