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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 8: Question number : 36 (page 567)

Use Exercise³¹to show that if, thenis.

Short Answer

Expert verified

The expressionis proved.

Step by step solution

Step by Step Solution

Step 1: Define the Recursive formula

A recursive formula is a formula that defines any term of a sequence in terms of its preceding terms.

Step 2: Solve by recursive procedure on

From exercise³¹, for andis a power of, thenfor constantsand.

Now given.

So,.

This gives

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Most popular questions from this chapter

Use generating functions to solve the recurrence relation $a_{k} = 7 a_{k - 1}$ with the initial condition $a_{0} = 5$ .

How many ternary strings of length six do not contain two consecutive $0' s$ or twoconsecutive $1' s$ ?

Suppose that in Example 8of Section 8.1a pair of rabbits leaves the island after reproducing twice. Find a recurrence relation for the number of rabbits on the island in the middle of the nth month.

Use Exercise 29 to show that if $a = b^{d}$ , then $f (n)$ is $O (n^{d} l o g n)$ .

For each of these generating functions, provide a closed formula for the sequence it determines.

a) ${(3x - 4)^3}$

b) ${\left( {{x^3} + 1} \right)^3}$

c) $1/(1 - 5x)$

d) ${x^3}/(1 + 3x)$

e) ${x^2} + 3x + 7 + \left( {1/\left( {1 - {x^2}} \right)} \right)$

f) $\left( {{x^4}/\left( {1 - {x^4}} \right)} \right) - {x^3} - {x^2} - x - 1$

g) ${x^2}/{(1 - x)^2}$

h) $2{e^{2x}}$

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Use Exercise³¹to show that if, thenis.

Short Answer

Step by step solution

Step by Step Solution

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Use Exercise31to show that if, thenis.

Short Answer

Step by step solution

Step by Step Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Decision Maths

Statistics

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use Exercise³¹to show that if, thenis.