- #1
Monochrome
- 11
- 0
Homework Statement
[tex]f(1)+f(2)...+f(n-1) =< \int_{0}^{n} f(x) dx =< f(2) +f(3)+...+f(n)[/tex]
is increasing and continuous on [1, inf)
I'm meat to prove the above, the idea I had was to use the trapezium rule to get an approximation of the integral, but since f''(x) can be either negative or positive I'm stuck as to how to do that. Also I'm in a first year course and I haven't yet learned about Bernoulli numbers or the like, which is what came up when I was looking around for this problem.
Edit: Would using left and right Riemann sums solve this? I can get the inequality but does increasing in this case mean non-decreasing?
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