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b. the sum of the first 55 is, compute 2k=1 ak• 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, . 6. Consider the recurrence relation an = an-1 - 2an-2 with first two terms ao = 0 and a1 = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. %3D

b. the sum of the first 55 is, compute 2k=1 ak• 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, . 6. Consider the recurrence relation an = an-1 - 2an-2 with first two terms ao = 0 and a1 = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 56EQ
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Please help with this discrete math question with details on how to do it. Need help with question #5. Thank you.  

4. Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E 1 ax. 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, .. 6. Consider the recurrence relation an = an-1 – 2an-2 with first two terms ao = 0 and aj = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. b. Solve the recurrence relation. That is, find a closed formula for a,. 7. Prove the following using induction. k3 = 13 + 23 + 33 + ...+ n³ = (1+2 +3 + …·+n)² k=1 n(n+1) [Hint: Recall that 1 + 2 + 3 + ..+n =
Transcribed Image Text:4. Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of sequence is this? b. Find the sum of the first 55 terms. That is, compute E 1 ax. 5. Use polynomial fitting to find a closed formula for the sequence (an)n e N,: 1,3, 11,31, 69, .. 6. Consider the recurrence relation an = an-1 – 2an-2 with first two terms ao = 0 and aj = 1. a. Write out the first 5 terms of the sequence defined by this recurrence relation. b. Solve the recurrence relation. That is, find a closed formula for a,. 7. Prove the following using induction. k3 = 13 + 23 + 33 + ...+ n³ = (1+2 +3 + …·+n)² k=1 n(n+1) [Hint: Recall that 1 + 2 + 3 + ..+n =
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