For the following summations from 1 to infinity, which tests for convergence would I use? I am confused on what to select.
1) 9/((n^2)*(sqrt(n)))
2) (-3*n*sqrt(n))/(n^2)
3) 3*(-1)^n
4) cos((n^5)+1)
5) (n^7)-10*n
Thanks
1) . You can apply the integral test, or recognize that it's a p-series, where (thus, the series converges).
2) . Again apply the integral test, or recognize it's a p-series, where (thus, the series diverges).
3) I forget how to prove it, but it diverges. (expanding we get 3-3+3-3+3-3+...)
4) . I believe you would use the limit comparison test here (?) : Thus, . Since this doesn't exist, then the series diverges. (I think this is correct)
5) . I'm sure the integral test would work here as well. It's pretty evident that the series diverges.
Can someone verify these??
oh so if i put any number as i get bigger it has to go close to zero?
also for the integral test, after you integrate, what value to you use as upper bound?
like for example this says n^2 + 7:
Visual Calculus -
i dont quite get the step after they say the integral becomes....
EDIT: ahh alright i get it