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vanmaiden
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Homework Statement
I've seen two methods that prove the integral test for convergence, but I fear they contradict each other. Each method uses an improper integral where the function f(x) is positive, decreasing, and continuous and f(x) = an. What confuses me is one method starts off the riemann sums at n = 1 and makes them all circumscribed rectangles - which make sense to me. The other method starts off the riemann sums at n = 0 and makes them all inscribed rectangles. Can anybody explain to me why each one of these work? Is one right and the other one wrong?
Homework Equations
The Attempt at a Solution
I've reviewed riemann sums in general, but I'm confused as to why two different methods are used in the theory behind the integral test.
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