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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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It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
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?
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.
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
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
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)
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.