(a) Given the recursive sequence aķ = ak-1 - k? +1 for all k > 1, and a1 = -4, find a2 and аз- (b) Compute the following sums using formulas from class. Do not try to compute something like 224. You may leave your answer in terms of big numbers like this. i. –23 + (-23)² +(-23)³ + ··. +(-23)1 75 ii. >ak if ar = 2k – 3 for all k > 1. Hint: Use properties of sums. k=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question
7.
Find the following. SHOW AND JUSTIFY YOUR WORK.
2
(a) Given the recursive sequence ak
- k2 +1 for all k > 1, and a1 =
-4, find
and
Ak-1
a2
a3.
(b) Compute the following sums using formulas from class. Do not try to compute something
like 224. You may leave your answer in terms of big numbers like this.
i. –23 + (-23)? +(-23)³ + · . + (-23)1
75
ii. E
ak if ak
= 2k – 3 for all k > 1. Hint: Use properties of sums.
||
k=1
Transcribed Image Text:7. Find the following. SHOW AND JUSTIFY YOUR WORK. 2 (a) Given the recursive sequence ak - k2 +1 for all k > 1, and a1 = -4, find and Ak-1 a2 a3. (b) Compute the following sums using formulas from class. Do not try to compute something like 224. You may leave your answer in terms of big numbers like this. i. –23 + (-23)? +(-23)³ + · . + (-23)1 75 ii. E ak if ak = 2k – 3 for all k > 1. Hint: Use properties of sums. || k=1
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