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Determine the following summation in terms of n: n2 E(2i + 5) i=1

Determine the following summation in terms of n: n2 E(2i + 5) i=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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8:50 FA2020 COТ3100 Но... Homework Assignment 4 COT3100 – Fall 2020 1) Determine the following summation in terms of n: n2 (2i + 5) i=1 2) Let g(n) be a function defined on the positive integers as follows: g(1) = 3, g(2) = 2, g(3) = 4 For n > 3,g(n) 3 9(n — 1) + 2g(п — 2) + 3g(n - 3) What are the values of g(4), g(5) and g(6)? If you would like to, for fun, write a computer program which prints out the first 1000 values of g(n) mod 10°+7. Feel free to include the source code inside the document your homework solutions. 3) Let n be a positive integer such that 7| (8" – 1). Prove that 7 | (8"+1 - 1). (Hint: Use a rule of powers to rewrite 8n+1. 4) Prove by induction that, for all positive integers n: п 2n3 + 11n? + 17n 3i2 + 8i + 4 = i=D1 5) Recall that the Fibonacci numbers are defined as follows: Fo = 0, F1 = 1 For n > 1, Fn = Fn-1+ Fn-2. Using induction on n, prove: F; = Fn+2 - 1 i=0 6) Give a summary of the academic contributions of Dr. Ingrid Daubechies. Be sure to include information about wavelets in your write up. Please aim for a length of roughly 200 - 400 words. Your summary must be typed. Please state the sources you used in writing your summary. 16 000 Dashboard Calendar Тo Do Notifications Inbox
Transcribed Image Text:8:50 FA2020 COТ3100 Но... Homework Assignment 4 COT3100 – Fall 2020 1) Determine the following summation in terms of n: n2 (2i + 5) i=1 2) Let g(n) be a function defined on the positive integers as follows: g(1) = 3, g(2) = 2, g(3) = 4 For n > 3,g(n) 3 9(n — 1) + 2g(п — 2) + 3g(n - 3) What are the values of g(4), g(5) and g(6)? If you would like to, for fun, write a computer program which prints out the first 1000 values of g(n) mod 10°+7. Feel free to include the source code inside the document your homework solutions. 3) Let n be a positive integer such that 7| (8" – 1). Prove that 7 | (8"+1 - 1). (Hint: Use a rule of powers to rewrite 8n+1. 4) Prove by induction that, for all positive integers n: п 2n3 + 11n? + 17n 3i2 + 8i + 4 = i=D1 5) Recall that the Fibonacci numbers are defined as follows: Fo = 0, F1 = 1 For n > 1, Fn = Fn-1+ Fn-2. Using induction on n, prove: F; = Fn+2 - 1 i=0 6) Give a summary of the academic contributions of Dr. Ingrid Daubechies. Be sure to include information about wavelets in your write up. Please aim for a length of roughly 200 - 400 words. Your summary must be typed. Please state the sources you used in writing your summary. 16 000 Dashboard Calendar Тo Do Notifications Inbox
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