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4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for n≥ 1, we have 1ª + 2ª +...+ (n − 1)ª ≤ "

4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for n≥ 1, we have 1ª + 2ª +...+ (n − 1)ª ≤ "

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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4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for rºdz, prove that for any integer n≥ 1, we have 1ª + 2ª + ... + (n − 1)ª ≤ f" zºdz ≤ 1 (b) Using part (a), or otherwise, prove that lim 11-400 r®d? <1^ +2^ +tna 1 +20 +..+na na+1 1 a +1'
Transcribed Image Text:4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for rºdz, prove that for any integer n≥ 1, we have 1ª + 2ª + ... + (n − 1)ª ≤ f" zºdz ≤ 1 (b) Using part (a), or otherwise, prove that lim 11-400 r®d? <1^ +2^ +tna 1 +20 +..+na na+1 1 a +1'
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