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4. Let a > 0 be a (fixed) real number. S (a) Using lower and upper Riemann sums for n ≥ 1, we have 1ª + 2ª + ... + (n − 1)ª ≤ [™" a r®dr <1* +2° +...+n. (b) Using part (a), or otherwise, prove that lim 818 radr, prove that for any integer 1a + 2a +...+na na+1 1 a +1

4. Let a > 0 be a (fixed) real number. S (a) Using lower and upper Riemann sums for n ≥ 1, we have 1ª + 2ª + ... + (n − 1)ª ≤ [™" a r®dr <1* +2° +...+n. (b) Using part (a), or otherwise, prove that lim 818 radr, prove that for any integer 1a + 2a +...+na na+1 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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4. Let a > 0 be a (fixed) real number. 'n (a) Using lower and upper Riemann sums for S n≥ 1, we have 1a + 2ª +... + (n - - 1)ª ≤ forh (b) Using part (a), or otherwise, prove that lim 84x xªdx, prove that for any integer r@dr <1 +2° +...+n“. 1a + 2a +...+ na na+1 1 a +1
Transcribed Image Text:4. Let a > 0 be a (fixed) real number. 'n (a) Using lower and upper Riemann sums for S n≥ 1, we have 1a + 2ª +... + (n - - 1)ª ≤ forh (b) Using part (a), or otherwise, prove that lim 84x xªdx, prove that for any integer r@dr <1 +2° +...+n“. 1a + 2a +...+ na na+1 1 a +1
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