Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 7, Problem 47E
To determine
To solve: The nonhomogeneous recurrence relation is
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For each of the following series, determine whether the absolute convergence series test
determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let
Mi = 4, while if the test determines absolute convergence let Mi
1 :
2:
∞
Σ(−1)"+¹ sin(2n);
n=1
Σ
n=1
Σ
((−1)”.
COS
n²
3+2n4
3: (+
4:
5 :
n=1
∞
n
2+5n3
ПП
n²
2 5+2n3
пп
n²
Σ(+)+
n=1
∞
n=1
COS
4
2 3+8n3
П
ηπ
n-
(−1)+1 sin (+727) 5 + 2m³
4
= 8.
Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is
-0.027
-0.621
-1.794
-1.132
-1.498
-4.355
-2.000
2.716
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.
Chapter 7 Solutions
Introductory Combinatorics
Ch. 7 - Prob. 1ECh. 7 - Prove that the nth Fibonacci number fn is the...Ch. 7 - Prove the following about the Fibonacci...Ch. 7 - 4. Prove that the Fibonacci sequence is the...Ch. 7 - By examining the Fibonacci sequence, make a...Ch. 7 - * Let m and n be positive integers. Prove that if...Ch. 7 - * Let m and n be positive integers whose greatest...Ch. 7 - Consider a 1-by-n chessboard. Suppose we color...Ch. 7 - Prob. 9ECh. 7 - Prob. 10E
Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - 13. Determine the generating function for each of...Ch. 7 - 14. Let S be the multiset {∞ · e1, ∞ · e2, ∞ · e3,...Ch. 7 - 15. Determine the generating function for the...Ch. 7 - 16. Formulate a combinatorial problem for which...Ch. 7 - 17. Determine the generating function for the...Ch. 7 - 18. Determine the generating function for the...Ch. 7 - 19. Let h0, h1, h2, …, hn, … be the sequence...Ch. 7 - Prob. 20ECh. 7 - 21. * Let hn denote the number of regions into...Ch. 7 - 22. Determine the exponential generating function...Ch. 7 - 23. Let α be a real number. Let the sequence h0,...Ch. 7 - 24. Let S be the multiset {∞ · e1, ∞ · e2, · , ∞ ·...Ch. 7 - 25. Let hn denote the number of ways to color the...Ch. 7 - Determine the number of ways to color the squares...Ch. 7 - Determine the number of n-digit numbers with all...Ch. 7 - Determine the number of n-digit numbers with all...Ch. 7 - We have used exponential generating functions to...Ch. 7 - Prob. 30ECh. 7 - Solve the recurrence relation hn = 4hn−2, (n ≥ 2)...Ch. 7 - Prob. 32ECh. 7 - Solve the recurrence relation hn = hn−1 + 9hn−2 −...Ch. 7 - Solve the recurrence relation hn = 8hn−1 − 16hn−2,...Ch. 7 - Solve the recurrence relation hn = 3hn − 2 − 2hn −...Ch. 7 - Prob. 36ECh. 7 - Determine a recurrence relation for the number an...Ch. 7 - Prob. 38ECh. 7 - Let hn denote the number of ways to perfectly...Ch. 7 - Let an equal the number of ternary strings of...Ch. 7 - * Let 2n equally spaced points be chosen on a...Ch. 7 - Solve the nonhomogeneous recurrence relation
Ch. 7 - Solve the nonhomogeneous recurrence relation
hn =...Ch. 7 - Solve the nonhomogeneous recurrence relation
Ch. 7 - Prob. 45ECh. 7 - Solve the nonhomogeneous recurrence relation
Ch. 7 - Solve the nonhomogeneous recurrence relation
Ch. 7 - Solve the following recurrence relations by using...Ch. 7 - (q-binomial theorem) Prove that
where
is the...Ch. 7 - Call a subset S of the integers {1, 2, …, n}...Ch. 7 - Solve the recurrence relation
from Section 7.6...Ch. 7 - Prob. 52ECh. 7 - Suppose you deposit $500 in a bank account that...
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- Class, the class silues, and the class notes, whether the series does alternate and the absolute values of the terms decrease), and if the test does apply, determine whether the series converges or diverges. For the ith series, if the test does not apply the let Mi = 2, while if the test determines divergence then M¿ = 4, and if it determines convergence then M¿ = 8. 1: 2: 3 : 4: 5 : ∞ n=1 ∞ (−1)n+1. Σ(-1) +1 n=1 ∞ п 3m² +2 Σ(-1)+1 sin(2n). n=1 ∞ 2n² + 2n +3 4n2 +6 1 e-n + n² 3n23n+1 9n² +3 In(n + 1) 2n+1 Σ(-1) +1 n=1 ∞ Σ(-1)". n=1 Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M4) + sin(M5) is 1.715 0.902 0.930 -1.647 -0.057 ● 2.013 1.141 4.274arrow_forward3. FCX14) = x²+3xx-y3 +.arrow_forwardBH is tangent to circle A and DF is a diameter. I don't know where to go from here. May you help please?arrow_forward
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