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Let t E Zt and let f : Z† → R be a function defined by n f(n) = k = 1* + 2' + 3* + ..+ n'. k=0 a) Show that f(n) = 0(n*+1). %3D b) Show that f(n) > / x' dx (Hint: think about the rectangles you might draw when first learning about definite integrals). c) Conclude that nt+1 = 0(f(n)).

Let t E Zt and let f : Z† → R be a function defined by n f(n) = k = 1* + 2' + 3* + ..+ n'. k=0 a) Show that f(n) = 0(n*+1). %3D b) Show that f(n) > / x' dx (Hint: think about the rectangles you might draw when first learning about definite integrals). c) Conclude that nt+1 = 0(f(n)).

Advanced Engineering Mathematics
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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Let t E Zt and let f : Z+ → R be a function defined by n f(n) = k = 1' + 2' + 3* + ...+ n°. k=0 a) Show that f(n) = 0(n*+1). n b) Show that f(n) > | x' dx (Hint: think about the rectangles you might draw when first learning about definite integrals). c) Conclude that n = 0(f(n)).
Transcribed Image Text:Let t E Zt and let f : Z+ → R be a function defined by n f(n) = k = 1' + 2' + 3* + ...+ n°. k=0 a) Show that f(n) = 0(n*+1). n b) Show that f(n) > | x' dx (Hint: think about the rectangles you might draw when first learning about definite integrals). c) Conclude that n = 0(f(n)).
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