Which is a true statement about infinite geometric series?

An infinite geometric series converges if −1. A finite geometric sequence will have an infinite geometric series. The graph of a convergent infinite geometric series goes to infinity.

What must be true in order to find a sum for an infinite geometric series?

To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r , where a1 is the first term and r is the common ratio. 8+12+18+27+… if it exists. Since r=32 is not less than one, the series does not converge.

What is the sum of a finite or infinite sequence?

and in this case the sum of the series is equal to 120. A finite series is given by all the terms of a finite sequence, added together. An infinite series is given by all the terms of an infinite sequence, added together. 1 2 + 1 4 = 3 4 .

How will you identify if the geometric series is finite or infinite?

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.

Is geometric series infinite?

In general, a geometric series is written as a + ar + ar2 + ar3 + , where a is the coefficient of each term and r is the common ratio between adjacent terms. Geometric series are among the simplest examples of infinite series and can serve as a basic introduction to Taylor series and Fourier series.

Is it true that some infinite geometric series have a sum?

If the common ratio r lies between −1 to 1 , we can have the sum of an infinite geometric series. That is, the sum exits for | r |<1 . An infinite series that has a sum is called a convergent series and the sum Sn is called the partial sum of the series.

What is the sum of infinite geometric series?

The formula for the sum of an infinite geometric series is S∞ = a1 / (1-r ).

What is the difference between finite and infinite series?

A sequence is a string of things in order. Finite sequences are sequences that end. Infinite sequences are sequences that keep on going and going.

Can the sum of an infinite geometric series be greater than 1?

The only possible answer would be infinity. So, we don’t deal with the common ratio greater than one for an infinite geometric series. If the common ratio r lies between − 1 to 1 , we can have the sum of an infinite geometric series.

How do you find the last term of an infinite geometric series?

Do It Faster, Learn It Better. 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 a 1 + a 1 r + a 1 r 2 + a 1 r 3 + , where a 1 is the first term and r is the common ratio.

What is the formula for the 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.

What is Infiniti geometric series?

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 a 1 + a 1 r + a 1 r 2 + a 1 r 3 +