8:50FA2020 COТ3100 Но...Homework Assignment 4COT3100 – Fall 20201) Determine the following summation in terms of n:n2(2i + 5)i=12) Let g(n) be a function defined on the positive integers as follows:g(1) = 3, g(2) = 2, g(3) = 4For 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 1000values of g(n) mod 10°+7. Feel free to include the source code inside the document yourhomework solutions.3) Let n be a positive integer such that 7| (8" – 1). Prove that 7 | (8"+1 - 1). (Hint: Use a rule ofpowers to rewrite 8n+1.4) Prove by induction that, for all positive integers n:п2n3 + 11n? + 17n3i2 + 8i + 4 =i=D15) Recall that the Fibonacci numbers are defined as follows:Fo = 0, F1 = 1For n > 1, Fn = Fn-1+ Fn-2.Using induction on n, prove:F; = Fn+2 - 1i=06) Give a summary of the academic contributions of Dr. Ingrid Daubechies. Be sure to include informationabout wavelets in your write up. Please aim for a length of roughly 200 - 400 words. Your summary mustbe typed. Please state the sources you used in writing your summary.16000DashboardCalendarТo DoNotificationsInbox

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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
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Inbox

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