Just started going over sequences, and was wondering why how these 2 problems are convergent. Thanks.
so u have
so it converge
for the second I don't see where u have any problems
same thing do as in first (maybe u have problems with " ") but i think it's not that, because you're doing sequences, and factorials must be done way more before sequences
Edit : this is wrong sorry
I pasted this same reply at the wrong place and got bit by the lion in the den. Here I am in the right place and doing it once again, just for you..
I can’t see what you posted, but if you want to know why the sequence converges, you can imagine 1 remains stationary, while the in the denominator increases at a much faster pace than the numerator , and eventually it converges to 0.
Once we know that it converges to 0, we can prove that with a given , there is a positive integer such that if , but we know that , so we can use to find n.
Since , which is equivalent to , which also is equivalent to , we are now ready to prove.
Let . Choose and let be any integer such that . Thus , and so .