series converge or diverge?
∞
Σ ((−1)^i*(i)^2)/(i^4)*-1
i=2
I have tryed using Alternating Series Test because when the sums are worked out eg i=2 (+) number where i-3 (-) number.
- But cant figure out where they Convergence OR Divergence.
- Is there another test i can use?
----------------------------------------------------------------------------
∞
Σ (n^2)/(2n +1)!
n=0
Can the ratio test be used?
I am quite confused....
you could also use the integral test(I'm saying this mainly because I like the integral test..even though in this case its hard =) so you need to determine if exists...you can evaluate this integral using partial fraction decomposition...so ..which is obviously ..therfore since the integral diverges the series diverges...I am sorry I was bored
Hello mathstud28
For your integral, it's far more simple to say that at infinite, the function inside the integral tends to infinity. Thus the integral is undefined.
The sole problem is that it was (2n+1)!, not only (2n+1).
This method is too complicated while a ratio test can give the answer. Although it's elegant, it's not judicious to use it.
Ratio test :
Which is always < 1, so the series converges
You quoted the integral test for doing a wrong thing, i haven't seen any disclaimer oO
I'm not sure to understand, what d'you want to say in this message ?
The lesser used tests can give some bad surprises, especially when you're not used to apply it, more especially when there is a test which is more simple !
you are saying I missed the fact that it was factorial...yeah you are right I do that a lot when its not LaTeX its hard to discern...nonetheless I was trying to give dimension to a problem that is generally one-dimensional...thanks for pointing out I missed the ! though!