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Question 52436: Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space. b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?.
Chapter 31 out of 37 from Discrete Mathematics for Neophytes: Number Theory, Probability, Algorithms, and Other Stuff by J. M. Cargal 2 Formula 1 The Finite Geometric Series The Finite Geometric Series The most basic geometric series is 1 + x + x2 + x3 + x4 + ... + xn.This is the finite geometric series because it has exactly n + 1 terms. It has a simple formula:.
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In zeta function regularization, the series ∑ = ∞ is replaced by the series ∑ = ∞ −.The latter series is an example of a Dirichlet series.When the real part of s is greater than 1, the Dirichlet series converges, and its sum is the Riemann zeta function ζ(s).On the other hand, the Dirichlet series diverges when the real part of s is less than or equal to 1, so, in particular, the. 6-.
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You can put this solution on YOUR website! To prove that: To prove it using induction: 1) Confirm it is true for n = 1 It is true since 1/2 = 1/2^1 2) Assume it is true for some value of n = k i.e. ----> eqn (1) 3) Now prove it is true for n = k+1 i.e. the sum up to (k+1) terms = 1 - 1/2^(k+1) Proof: For n = k+1, the expression of the sum is: = ---> from eqn(1) = ---> taking common denominator.