1. 2. 3. 4. Find the generating function for the number of non-negative integer solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha to find the number of solutions when n = 30. You will need to use the following command taylor series [insert generating function here] order 30 at x=0 Let n be a nonnegative integer. Find the generating function for the number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and 0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4. Use WolframAlpha to find the number of solutions when n = = 30. Find the exponential generating function for the number of permutations with repetition of length n of the set {a, b, c}, in which there are an odd number of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to find the number of such permutations when n = 10. Find the generating function for the number of partitions of an integer into distinct even parts. Use Wolfram Alpha to find the number of partitions of 15 into distinct even parts.
1. 2. 3. 4. Find the generating function for the number of non-negative integer solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha to find the number of solutions when n = 30. You will need to use the following command taylor series [insert generating function here] order 30 at x=0 Let n be a nonnegative integer. Find the generating function for the number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and 0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4. Use WolframAlpha to find the number of solutions when n = = 30. Find the exponential generating function for the number of permutations with repetition of length n of the set {a, b, c}, in which there are an odd number of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to find the number of such permutations when n = 10. Find the generating function for the number of partitions of an integer into distinct even parts. Use Wolfram Alpha to find the number of partitions of 15 into distinct even parts.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Question
Answer only 4
![1.
2.
3.
4.
Find the generating function for the number of non-negative integer
solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha
to find the number of solutions when n = 30. You will need to use the following
command
taylor series [insert generating function here] order 30 at x=0
Let n be a nonnegative integer. Find the generating function for the
number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and
0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4.
Use WolframAlpha to find the number of solutions when n =
= 30.
Find the exponential generating function for the number of permutations
with repetition of length n of the set {a, b, c}, in which there are an odd number
of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to
find the number of such permutations when n = 10.
Find the generating function for the number of partitions of an integer
into distinct even parts. Use Wolfram Alpha to find the number of partitions of
15 into distinct even parts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed04f254-2b14-4f51-a897-ea8ba8024a7a%2F42e2c4ad-705e-450d-85d2-0b2e266f4cad%2Fw9vgt9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
2.
3.
4.
Find the generating function for the number of non-negative integer
solutions to 2x+3y+5z = n, where n is a nonnegative integer. Use WolframAlpha
to find the number of solutions when n = 30. You will need to use the following
command
taylor series [insert generating function here] order 30 at x=0
Let n be a nonnegative integer. Find the generating function for the
number of solutions to x1+x2+x3 + x4 = n, where x1, x2, x3, x4 are integers and
0x1, 3≤ x2 < ∞0, 2x3 ≤5 1≤ x ≤4.
Use WolframAlpha to find the number of solutions when n =
= 30.
Find the exponential generating function for the number of permutations
with repetition of length n of the set {a, b, c}, in which there are an odd number
of a's, an odd number of b's, and an even number of c's. Use WolframAlpha to
find the number of such permutations when n = 10.
Find the generating function for the number of partitions of an integer
into distinct even parts. Use Wolfram Alpha to find the number of partitions of
15 into distinct even parts.
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