Mathematics · Real Analysis
Consider the identity function f(x) = x on I := [0, 1]. Let P n be the partition that divides I into n equal parts. If U(f, P n ) and L(f, P n ) are the upper and lower Riemann sums, respectively, and A n = U(f, P n ) - L(f, P n ), then which of the following is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1lim n→∞ nA n = 0
- 2∑ n=1 ∞ A n is convergent
- 3A n is strictly monotonically decreasing✓
- 4∑ n=1 ∞ A n A n+1 = 1
Correct answer
A n is strictly monotonically decreasing
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