==4. Let a > 0 be a (fixed) real number.(a) Using lower and upper Riemann sums forS™n ≥ 1, we have1a + 2a +rn+ (n − 1)² ≤ f"(b) Using part (a), or otherwise, prove that1a + 2a +limn→∞na+1xªdx, prove that for any integerxadx ≤ 1ª + 2a ++ na1a +1+na.===

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Answered: . Let a > 0 be a (fixed) real number.…

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 n≥ 1, we have 1° +2° +...+(n-1) < ["ha (b) Using part (a), or otherwise, prove that 1a + 2a +. na+1 on S xadx, prove that for any integer 0 lim n→∞ xadx ≤ 1ª + 2ª +...+na. + na 1 a + 1