How do you tell if a geometric series converges or diverges?

How do you tell if a geometric series converges or diverges?

In fact, we can tell if an infinite geometric series converges based simply on the value of r.When |r| x26lt; 1, the series converges. When |r| u2265 1, the series diverges. This means it only makes sense to find sums for the convergent series since divergent ones have sums that are infinitely large.

How do you find where a geometric series converges?

The convergence of the geometric series depends on the value of the common ratio r:

  • If |r| x26lt; 1, the terms of the series approach zero in the limit (becoming smaller and smaller in magnitude), and the series converges to the sum a / (1 – r).
  • If |r| 1, the series does not converge.
  • What does convergent mean in geometric series?

    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.

    Can you find the sum of a divergent geometric series?

    Divergent series are weird. They certainly don’t have a sum in the traditional sense of the wordthat is, their partial sums do not converge (by definition). That said, there are various extensions of the classical notion of sum that assign values to divergent sums as well.

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