A sequence is a function whose domain is the set of natural number. A sequence $s_1,s_2\dots$ of real numbers is said to have a $\text{ limit }l\text{ if }lim{s}_n=l\text{. If }l<\mathrm{\infty }\text{, then }<s_n>$ is said to convergent. The following are well known

(i) $\underset{n\to \mathrm{\infty }}{lim} 1/n^p=0(p>0)$

(ii) $\underset{n\to \mathrm{\infty }}{lim} x^n=0\left(\right|x|<1)$

(iii) $\text{ If }\underset{n\to \mathrm{\infty }}{lim} s_n=l\text{, then }\underset{\to \mathrm{\infty }}{lim} \frac{s_1+s_2+\dots \dots +s_n}{n}=l$