today we will go over sequence of numbers and limit.

Let $a_1, a_2, \cdots $ be a sequence of numbers. We can have many examples of it.

• $1,-1,1,-1\cdots $
• $0.9,0.99, 0.999, $
• $1,2,3, \cdots, $

We say a sequence $(a_n)$ converges to $a$, if for any $\epsilon>0$, there exists $N>0$, such that for any $n > N$, we have $|a_n - a| \leq \epsilon$.

a series is something that looks like $\sum_{n=1}^\infty a_n$. We can define the partial sum $S_n = \sum_{j=1}^n a_j$. We say the series $\sum_n a_n$ convergers if and only the partial sum converges.

Series is like a discretized version of integral.