Message Boards Message Boards

1
|
2451 Views
|
2 Replies
|
2 Total Likes
View groups...
Share
Share this post:

Entering a limit of sum product into Wolfram|Alpha?

B B
Posted 2 years ago

Hello,

I'm new to wolframalpha.com, not sure I am in the right place to ask this question, apologies if. I just want to know if Wolfram|Alpha is able to calculate this limit, to know if the sum product converges or not:

$\lim_{m\rightarrow\infty} \sum_{n=1}^{m} n^{-0.5} \cos(\ln(n)) \sum_{n=1}^{m} (-1)^{n} n^{-0.5} \cos(\ln(n))$

The LateX may not work...

This is the "code" I enter, is it correct, please?

lim( sum( n^{-0.5} * cos( ln(n) ) ,n,1,m ) * sum( (-1)^{n} *n^{-0.5} * cos(ln(n)) ,n,1,m),m,inf)

What should I modify, please? Because it gives something else like "Interpreting as: cos", or it may be too much for the machine?
POSTED BY: B B
2 Replies
Sort By:
Bill Nelson
Bill Nelson
Posted 2 years ago

This

sum((-1)^n/sqrt(n)*cos(ln(n)),{n,1,4000})

WolframAlphaInput

seems to strongly hint that will contribute a factor of about -0.643 to the result.

This

sum(1/sqrt(n)*cos(ln(n)),{n,1,4000})

WolframAlphaInput

does not strongly hint what that sum will be, but runs out of time for larger n.

Wait to see if the graphs appear after it says it has run out of time doing the calculations.

This

lim 1/n as n->infinity

is the notation that Wolfram|Alpha usually understands when trying to enter a limit

but I have not been able to coax Wolfram|Alpha into finding your limit.

Part of the problem may be that Sum may be expecting your n to be an integer but that Lim is not expecting m to be an integer
POSTED BY: Bill Nelson
B B
B B
Posted 2 years ago

Anyway Bill, thanks for your help.

Might someone else have any additional ideas?
POSTED BY: B B
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract