How do you know if a series is convergent or divergent?

Ratio test. If r < 1, then the series is absolutely convergent. If r > 1, then the series diverges. If r = 1, the ratio test is inconclusive, and the series may converge or diverge.

What is convergence in maths?

Convergence, in mathematics, property (exhibited by certain infinite series and functions) of approaching a limit more and more closely as an argument (variable) of the function increases or decreases or as the number of terms of the series increases.

What is meant by convergence of series?

A series is the sum of a sequence. If it is convergent, the sum gets closer and closer to a final sum.

What is convergence and divergence in series?

If the sequence of partial sums is a convergent sequence (i.e. its limit exists and is finite) then the series is also called convergent and in this case if limn→∞sn=s lim n → ∞ ⁡ s n = s then, ∞∑i=1ai=s ∑ i = 1 ∞ a i = s . ... Therefore, the sequence of partial sums diverges to ∞ ∞ and so the series also diverges.

Is 0 convergent or divergent?

Why some people say it's true: When the terms of a sequence that you're adding up get closer and closer to 0, the sum is converging on some specific finite value. Therefore, as long as the terms get small enough, the sum cannot diverge.

How do you know which convergence test to use?

If you see that the terms an do not go to zero, you know the series diverges by the Divergence Test. If a series is a p-series, with terms 1np, we know it converges if p>1 and diverges otherwise. If a series is a geometric series, with terms arn, we know it converges if |r|