Let n be a positive integer. Prove the following: (i) 1³ +2³+ · +n³ = (1+2+3+…+n)². (Use induction on n)
Let n be a positive integer. Prove the following: (i) 1³ +2³+ · +n³ = (1+2+3+…+n)². (Use induction on n)
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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Transcribed Image Text:Let n be a positive integer. Prove the following:
(i) 1³ +2³+
•+n³
η
=
(1+2+3+ •+n)². (Use induction on n)
(ii) Prove or give a counter example: 2" <n! for all positive integers n
(iii) Prove or give a counter: We can find a number m such that 2n <n! for all positive
integers n > m. Note that if you say it is true, then you need to find m AND you need to
prove the inequality.
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