4. Prove that (a + b) ≤a+b≤ a + b for any real numbers a and b. (Hint: Use cases when a, b ≥ 0; a, b < 0; and a & b have different signs.)
4. Prove that (a + b) ≤a+b≤ a + b for any real numbers a and b. (Hint: Use cases when a, b ≥ 0; a, b < 0; and a & b have different signs.)
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:4. Prove that -(lal+ |6|) < a +b< |a| + [b| for any real numbers a and b.
(Hint: Use cases when a, b > 0; a, b < 0; and a & b have different signs.)
5.
Prove the triangle inequality given by la + b| < la| + 16|.
6. Use mathematical induction to show that for any positive integer n,
(1+2+ .+n)² = 1³ + 2° + ... + n°.
(Hint: Apply binomial expansion)
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