Given: 0<a<=1/4 An = n^(2n) * (2a)^n ----------------- (2n)! ...determine whether this sequence in convergent. Determine what happens when a=1/4. In the case this sequence is non-convergent, demonstrate it by using 2 subsequences whose limits are different to each other.
Then I typed in (in the ClassPad):
lim n^(2n) * (2a)^n ----------------- n->+inf (2n)!
But the classpad didn't give me any solution to this.The classpad just delayed almost a minute and then it returned the same expression without calculating limit. I think the problem is how does the CP to solve factorial expressions algebraically, that's to say, as everybody of us know, something like:
n! n! 1 ------ = ------- => simplify and then ------- (n+1)! (n+1)n! (n+1)
What do you say about all this?
Can I define my own factorial function in the classpad giving the following rules?
0! = 1
1! = 1
n! = n(n-1)!
Thanks in advance...