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Q: How can you tell if a infinite geometric series has a sum or not?

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It depends on the series.

The sum of the series a + ar + ar2 + ... is a/(1 - r) for |r| < 1

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Eight. (8)

-20

Partial sum is a sum of part of the infinite series. However, series is called a sum of all the terms in infinite series. Hence partial sum is a finite series.

What is the assembly program to generate a geometric series and compute its sum The inputs are the base root and the length of the series The outputs are the series elements and their sum?

1,944 = 1296 x 1.5

It's a geometric progression with the initial term 1/2 and common ratio 1/2. The infinite sum of the series is 1.

The Nth partial sum is the sum of the first n terms in an infinite series.

Yes, the sum of infinite ones equal the sum of infinite twos.

"e" is known as EULER'S NUMBER."e" is the sum of an infinite geometric series = 1 + 1/1! + 1/2! + 1/3! + 1/4! ........ = approx 2.7182818284590452353603

An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.

No.

The sum of every odd number is infinite.

1/8

"e" is known as EULER'S NUMBER."e" is the sum of an infinite geometric series = 1 + 1/1! + 1/2! + 1/3! + 1/4! ........ = approx 2.718Read more: In_math_what_does_e_stand_for

160... I think. The series is 80+40+20+10+5+2.5+............ (Given the series is infinite it never ends but it gets pretty close to 160) = 159.99999999... ad infinitum [For future reference... series like this are basically equal to 2*the highest value e.g. 2*80=160]

-75.25

The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.

The sum is infinite

an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.

The geometric distribution is: Pr(X=k) = (1-p)k-1p for k = 1, 2 , 3 ... A geometric series is a+ ar+ ar2, ... or ar+ ar2, ... Now the sum of all probability values of k = Pr(X=1) + Pr(X = 2) + Pr(X = 3) ... = p + p2+p3 ... is a geometric series with a = 1 and the value 1 subtracted from the series. See related links.

Those terms are both used to describe different kinds of infinite series. As it turns out, somewhat counter-intuitively, you can add up an infinitely long series of numbers and sometimes get a finite sum. And example of this is the sum of one over n2 where n stands for the counting numbers from 1 to infinity. It converges to a finite sum, and is therefore a convergent series. The sum of one over n is a divergent series, because the sum is infinity.

Your question is ill-posed. Is there a particular formula (e.g., \sum_{i=0}^{n-1} a r^i = a(1-r^n)/(1-r)) that you're trying to prove? If so, this page may be some help: http://www.mathalino.com/reviewer/derivation-of-formulas/sum-of-finite-and-infinite-geometric-progression