This problem appears on a practice final my professor gave out and I'm not sure what to do. Could someone show me how to do this limit?
Let f be continuous on the interval [0,1]. Show that:
lim as n approaches infinity of
(1/n) * [summation from k=1 to n of ((-1)^k)*[(f(k/n) - (f((k-1)/n)]]
equals zero.
I hope you can understand what I wrote. Thanks for any help you can offer.
Let f be continuous on the interval [0,1]. Show that:
lim as n approaches infinity of
(1/n) * [summation from k=1 to n of ((-1)^k)*[(f(k/n) - (f((k-1)/n)]]
equals zero.
I hope you can understand what I wrote. Thanks for any help you can offer.