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

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

Because series converges

We have to show that

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

Then

L=0+

Hence,

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.

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