# Thread: converges to zero prove

1. ## converges to zero prove

I would appreciate some help with the following.
For each of the following sequences state whether it converges to zero, and prove your answer. [A strategy is acceptable as a proof. proofs based on results from Calculus I or II are not acceptable.]
a). a) x_n from n=1 to infinity, given by x_n=1/n! for all n.

2. Originally Posted by charikaar
I would appreciate some help with the following.
For each of the following sequences state whether it converges to zero, and prove your answer. [A strategy is acceptable as a proof. proofs based on results from Calculus I or II are not acceptable.]
a). a) x_n from n=1 to infinity, given by x_n=1/n! for all n.
Use the fact that $2^n < n!$ for $n \ge 4$ so $\frac{1}{n!} < \frac{1}{2^n}$ .