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?
dontdont9
May 16, 2022, 1:35pm
2
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
Anyway Bill, thanks for your help.
Might someone else have any additional ideas?