Question

If a series converges, then the sequence of partial sums of the series also converges. True False Submit Answer 10. –/1 points My Notes If a series an converges, then the terms an tend to zero as n increases. True False

Answer 1

Answer:

True

True

Step-by-step explanation:

We are given that a series converges

We have to check that if series converges then the sequence of partial sum converges

Let $\sum_{k=1}^{n}a_n=L$

Because series converges

We have to show that $\sum_{k=1}^{n-1}a_n=L$

When series converges then the nth term tends to zero.It is a sufficient condition .

Then $\sum_{k=1}^{n}a_n=a_n+\sum_{k=1}^{n-1}a_n$

L=0+$\sum_{k=1}^{n-1}a_n$

Hence, $\sum_{k=1}^{n-1}a_n=L$

Therefore, if a series converges then the sequence of partial sum also converges is true.

If a series converges then the nth term tends to zero as n increases  .It is a sufficient condition for series convergence .Hence, the statement is true.