Does the Integral Test Result Indicate the Series Sum?

[rick906]

Hi all,
I just want to know a little something:
When doing the integral test in order to find a sum, when might get a result (integral) of a certain number. As we know, getting a number as result an integral test means that this serie converges...but does that mean that the serie converges to this (the result of the integral...number we just found)?
I don't think so, but I'm not sure either.

Thanks for the info

 

[uman]

No it does not.

 

[rick906]

Thanks for the fast reply dude!

If that number is not the sum, does it represent something?
(just outta curiosity)
Thank you

 

[lurflurf]

If that number is not the sum, does it represent something?
(just outta curiosity)

It is a first approximations of the sum.
For example say we desired to know
log(n!)=sum[log(k),{k,1,n}]~Integral[log(k),{k,0,n}]~n*log(n)-n
other integrals can be used for better approximations