Use the epsilon N definition to prove that the sequence 1n f

Use the \"epsilon, N definition\" to prove that the sequence {1/n!} for n=1 to infinity, converges to zero.

Solution

Consider the sequence 1/n!

As n tends to infinity n >M for a large M

Hence 1/n! < 1/M!

As M is large 1/M(M-1)(M-2)....1 <epsilon for a small positive value epsilon

Hence converges to 0

Proved