Calculus Homework

[MrCodeDude]

Determine the convergence or divergence of the sequence with the given general term
15. a sub n = ( sin [ sqrt[n] ] ) / sqrt[n]

How do I get rid of the sin?

Find the sum of the series
25. E (sum of the sequence) as the limit approaches infinity, starting value is 0 ( 1 / 2^x - 1 / 3^x )

I thought I could just evaluate each limit seperately, where both converge to 0, and thus the answer would be Converge to 0. But no, it converges to 1/2.

Help on either would be greatly appreciated.

 

[olds]

Originally posted by: MrCodeDude
How do I get rid of the sin?
Help on either would be greatly appreciated.

Bible

 

[Yossarian]

my interest is diverging from your thread.

 

[OverVolt]

1+1=2

glad i could help.

 

[Triforceofcourage]

So glad I am done with calculus 🙂 Sorry my post was practically useless. lol

 

[sharkeeper]

quote:
Originally posted by: MrCodeDude
How do I get rid of the sin?
Help on either would be greatly appreciated.


Bible

:laugh:

 

[MrCodeDude]

Originally posted by: oldsmoboat

Originally posted by: MrCodeDude
How do I get rid of the sin?
Help on either would be greatly appreciated.

Bible

So I should bring a bible to class and repent all the sin's on my math test?

 

[MrCodeDude]

bump.

 

[Legendary]

For 15., when you consider that the numerator will never be > 1, it should be apparent that it converges to 0.

You can use one of the convergence tests to show this.

 

[MrCodeDude]

Originally posted by: Legendary
For 15., when you consider that the numerator will never be > 1, it should be apparent that it converges to 0.

You can use one of the convergence tests to show this.

Thanks, yeah, I used Squeeze's Theorem.

 

[pray4mojo]

nm, too slow

 

[Howard]

You'd get better help if you wrote out the problem. I'm too lazy to try to figure out what you said. 🙂

 

[slpaulson]

For number 15, look up geometric series.

They aren't asking what the items converge to, they are asking what the sum converges to.

The other question is at most plus or minus 1/sqrt(n). What is this if n is infinity?

 

[desteffy]

for the first the top one you can bound the sin by one, so it will converge since the same seq with a 1 in the top converges (could be called "comparison test" depending on your book)

second split it into two sequences and then evaluate each one as a geometric sequence

 

[pray4mojo]

You can separate 25.
Use the equation a1 / (1 - r)

Ratio of 1/2^x = 1/2
First term of 1/2^x = 1
Therefore it converges to 2

Ratio of 1/3^x = 1/3
First term of 1/3^x = 1
Therefore it converges to 3/2.

2 - 3/2 = 1/2