This can be seen either by applying the master theorem or by observing that the times for the recursive subproblems decrease in a geometric series.
42.
Appears similar to an arithmetico-geometric series with common difference of 1 and common ratio of \ frac { 1 } { 7 }.
43.
But on closer inspection does not seem to be an arithmetico-geometric series as the n appears on the denominator instead of the numerator.
44.
We can then show that the series converges absolutely by showing that its terms will eventually become less than those of a certain convergent geometric series.
45.
Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series.
46.
So in a certain sense the exponential series is an instance of the geometric series .-- a 08 : 39, 14 January 2012 ( UTC)
47.
Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.
48.
Book IX, Proposition 35 of Euclid's " Elements " expresses the partial sum of a geometric series in terms of members of the series.
49.
If ? " x " is small then, as a first-order approximation of the geometric series equation ( 4 ) can be written as:
50.
The last equality arises from the infinite geometric series and the equality only holds if | 0.5 " z " " 1 | 0.5.
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