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.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.