Chapter B, Problem 3AYU

To determine

To fill: If the sequence $\left\{s_n\right\}$ of partial sums of an infinite series ${\displaystyle \sum _{k = 1}^{\infty }{a}_k}$ has a limit $\text{S}$, then the series _________.

Answer to Problem 3AYU

Solution:

If the sequence $\left\{s_n\right\}$ of partial sums of an infinite series ${\displaystyle \sum _{k = 1}^{\infty }{a}_k}$ has a limit $\text{S}$, then the series converges and is said to have the sum $\text{S}$.

Explanation of Solution

If the sequence $\left\{s_n\right\}$ of partial sums of an infinite series ${\displaystyle \sum _{k = 1}^{\infty }{a}_k}$ has a limit $\text{S}$, then the series converges and is said to have the sum $\text{S}$.