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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
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.
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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.
It depends on the series.
The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.
The sum of the series a + ar + ar2 + ... is a/(1 - r) for |r| < 1
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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?
It's a geometric progression with the initial term 1/2 and common ratio 1/2. The infinite sum of the series is 1.
1,944 = 1296 x 1.5
The sum to infinity of a geometric series is given by the formula Sā=a1/(1-r), where a1 is the first term in the series and r is found by dividing any term by the term immediately before it.
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
For a number to be rational you need to be able to write it as a fraction. To answer your question, it must repeat as a decimal or else terminate which can be thought of as repeating zeroes. Further, every repeating decimal can be written as a fraction and you can find the fraction by using the formula for the sum of an infinite geometric series.
The formula to find the sum of a geometric sequence is adding a + ar + ar2 + ar3 + ar4. The sum, to n terms, is given byS(n) = a*(1 - r^n)/(1 - r) or, equivalently, a*(r^n - 1)/(r - 1)