What if r is greater than 1 geometric series?

If |r| < 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. When r = 1, all of the terms of the series are the same and the series is infinite.

How do you find the sum of an infinite geometric series if r is greater than 1?

So, if you replace rn with 0 in the summation formula, the 1-rn part just becomes 1, and the numerator just becomes a1. The formula for the sum of an infinite geometric series is S∞ = a1 / (1-r ).

What is r in a geometric sequence?

Recall that a geometric sequence is a sequence in which the ratio of any two consecutive terms is the common ratio, r.

What is r in infinite geometric series?

An infinite geometric series is the sum of an infinite geometric sequence . This series would have no last term. The general form of the infinite geometric series is a1+a1r+a1r2+a1r3+… , where a1 is the first term and r is the common ratio.

Do all geometric series converge?

Geometric Series. These are identical series and will have identical values, provided they converge of course.

How do you know if it’s a geometric sequence?

How To: Given a set of numbers, determine if they represent a geometric sequence.

Divide each term by the previous term.
Compare the quotients. If they are the same, a common ratio exists and the sequence is geometric.

How do you tell if a geometric series is infinite or finite?

A geometric series is an infinite series whose terms are in a geometric progression, or whose successive terms have a common ratio. If the terms of a geometric series approach zero, the sum of its terms will be finite.

Which is an example of a geometric series?

A geometric series is a series whose related sequence is geometric. It results from adding the terms of a geometric sequence . Example 1: Finite geometric sequence: Related finite geometric series: 1 2 + 1 4 + 1 8 + 1 16 + + 1 32768. Written in sigma notation: 15 ∑ k = 1 1 2k. Example 2:

When is the common ratio greater than one in an infinite geometric series?

But in the case of an infinite geometric series when the common ratio is greater than one, the terms in the sequence will get larger and larger and if you add the larger numbers, you won’t get a final answer. The only possible answer would be infinity. So, we don’t deal with the common ratio greater than one for an infinite geometric series.

When does a geometric series grow to infinity?

So, when the common ratio is greater than 1, the Nth term of a Geometric Sequence will also grow towards infinity as N gets larger. Therefore a Geometric Series with an “R” greater than 1 will grow towards infinity with each additional term. However, when the absolute value of the common ratio is between -1 and 1, a special situation arises.

How to find the sum of a finite geometric series?

Finite Geometric Series. To find the sum of a finite geometric series, use the formula, Sn = a1(1 − rn) 1 − r, r ≠ 1 , where n is the number of terms, a1 is the first term and r is the common ratio . Example 3: Find the sum of the first 8 terms of the geometric series if a1 = 1 and r = 2 . S8 = 1(1 − 28) 1 − 2 = 255. Example 4:

What if r is greater than 1 geometric series? If |r| < 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. When r = 1, all…