Simplifying e^(1/(n+1))/e^(1/n) for the ratio test

[Jac8897]

Homework Statement

e^(1/n+1)/e^(1/n)

Homework Equations

this is for a series test "ratio test" I need to simplify it I went blank in this part


thanks

The Attempt at a Solution

 

[Quantumpencil]

the sum from 1 to infinity I'm guessing?

What are you trying to show?

 

[Jac8897]

i got the answer that this series converges because any number multiply by 0 = 0 but i want to know how to deal with that part look at my attachment

this is the ratio test for calc 2 [An+1/An]

 

[Office_Shredder]

Do you know how to simplify

a^k/a^j by combining their exponents?

 

[Jac8897]

is it a^(k-J)

 

[Office_Shredder]

So here a=e and what are k and j?

 

[Jac8897]

so e^(1/n+1)-(1/n)
can i do this ?
(1/n+1)-(1/n)

lcd (n+1)(n)
(n^2+n)

so e^(n^2+n)

 

[Office_Shredder]

I think there are some missing parentheses

By (1/n+1) do you mean 1/(n+1)?

You definitely did not do 1/(n+1)-1/n correctly (or 1/n+1-1/n as order of operations would have it be). Why would you just multiply their denominators?

 

[Jac8897]

sorry I see what i did wrong I attached a picture of what I think would be the correct way can you double check it

thank you

 

[Office_Shredder]

If you post an attachment we have to wait for it to be approved. You might want to put it up at imageshack.us or something and then give us a link to it to make it go faster

 

[Jac8897]

http://img694.imageshack.us/img694/5802/homework1.png

ok thanks for the website

 

[Jac8897]

I have to go I will check you replay in one hour thanks for the help

 

[rickz02]

Check the subtraction of the fractions in the exponent.