1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.
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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1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.
2. Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a
3. Prove that for all natural numbers k, a (5*2^(2k+1) - 1)/3 + a*4^k is of the form 5 + 6a.
I need help in all of those three questions please.
Proof by induction.
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Follow-up Question
Prove that for all natural numbers k, a (5*2^(2k+1) - 1)/3 + a*4^k is of the form 5 + 6a.
Can you see if this question allowed to be proved by induction? I hope it is not similar to that of the previous one that I asked...
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Follow-up Question
Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a
Solution
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