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Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for S xdx, prove that for any integer n≥ 1, we have 10 +2 +...+(n - 1)*s "ard 1+2 +...+n (b) Using part (a), or otherwise, prove that lim 11-700 19+20 tot n 1 a +1

Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for S xdx, prove that for any integer n≥ 1, we have 10 +2 +...+(n - 1)*s "ard 1+2 +...+n (b) Using part (a), or otherwise, prove that lim 11-700 19+20 tot n 1 a +1

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 a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for S™ n> 1, we have 1ª + 2a +...+ (n − 1) < ≤ f zºdz (b) Using part (a), or otherwise, prove that lim n→∞ xdx, prove that for any integer r®d <1* +2 +...+na. 1ª + 2ª +...+na na+1 a +1
Transcribed Image Text:Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for S™ n> 1, we have 1ª + 2a +...+ (n − 1) < ≤ f zºdz (b) Using part (a), or otherwise, prove that lim n→∞ xdx, prove that for any integer r®d <1* +2 +...+na. 1ª + 2ª +...+na na+1 a +1
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