Mathematics: A Discrete Introduction - 3 Edition - Chapter 18 - Problem 18.19
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# Assume that the Negative Binomial Theorem (Theorem 18.10) extends to any negative real

Mathematics: A Discrete Introduction | 3rd Edition

Problem 18.19

Assume that the Negative Binomial Theorem (Theorem 18.10) extends to any negative real number to develop an infinite series for 1 p 1 x : Then, substitute x D 1 2 into your formula through to the x 5 term to compute an approximation to p 2. How good is this approximation?

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Week 2 Notes Calc II N  Summation Notation; ∑ f (x) i=i  Used for adding a lot of numbers or series of numbers with a pattern.  Ex: 1+2+3+4+…+100 (easy to see pattern)  Ex: .5+2+4.5+8+…+128 (not easy to see clear pattern) N ∑ f (x)  i=i is a better way of writing these long patterned lists. 16i2 12 22 32 162  Ex: ∑ = + + +…+ =748 (this is the same i=12 2 2 2 2 pattern from above that didn’t seem to have a clear pattern)  Properties of Summation Notation n n ai+¿∑ bi=∑ (i +i ) i=1 i=1 

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