What does it mean if the limit of a series is 0?

If the limit is zero, then the bottom terms are growing more quickly than the top terms. Thus, if the bottom series converges, the top series, which is growing more slowly, must also converge. If the limit is infinite, then the bottom series is growing more slowly, so if it diverges, the other series must also diverge.

What does it mean to converge to 0?

For example, the function y = 1/x converges to zero as x increases. Although no finite value of x will cause the value of y to actually become zero, the limiting value of y is zero because y can be made as small as desired by choosing x large enough. The line y = 0 (the x-axis) is called an asymptote of the function.

How do you tell if an infinite series converges or diverges?

Starts here16:18Convergence and Divergence – Introduction to Series – YouTubeYouTubeStart of suggested clipEnd of suggested clip60 second suggested clipIf you want to determine if the sequence is convergent or not we need to do is take the limit as nMoreIf you want to determine if the sequence is convergent or not we need to do is take the limit as n approaches infinity of the sequence a sub n. And if it’s equal to a constant.

What happens if the ratio test equals 0?

r = 0 implies the power series is convergent for all x values, and r = ∞ implies the power series is divergent always. Again we have the case that r = 0 < 1, hence we can conclude that the power series converge for all x values.

Is the limit of a convergent series always 0?

Apparently if a series is convergent the limit is always zero.

What does it mean for an infinite sequence to converge?

Infinite sequences and series continue indefinitely. A series is said to converge when the sequence of partial sums has a finite limit. A series is said to diverge when the limit is infinite or does not exist.

What does it mean to say that an infinite series converges?

A series is convergent (or converges) if the sequence of its partial sums tends to a limit; that means that, when adding one after the other in the order given by the indices, one gets partial sums that become closer and closer to a given number.

What is the meaning of infinite series?

infinite series, the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are useful in mathematics and in such disciplines as physics, chemistry, biology, and engineering.