. 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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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==
4. Let a > 0 be a (fixed) real number.
(a) Using lower and upper Riemann sums for
S™
n ≥ 1, we have
1a + 2a +
rn
+ (n − 1)² ≤ f"
(b) Using part (a), or otherwise, prove that
1a + 2a +
lim
n→∞
na+1
xªdx, prove that for any integer
xadx ≤ 1ª + 2a +
+ na
1
a +1
+na.
===
Transcribed Image Text:== 4. Let a > 0 be a (fixed) real number. (a) Using lower and upper Riemann sums for S™ n ≥ 1, we have 1a + 2a + rn + (n − 1)² ≤ f" (b) Using part (a), or otherwise, prove that 1a + 2a + lim n→∞ na+1 xªdx, prove that for any integer xadx ≤ 1ª + 2a + + na 1 a +1 +na. ===
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