Riemann-sums

[Little]

a) Give the definition of upper and lower Riemann sums U(f, P) og L(f, P), where f is a limited function on an intervall [a, b] and P is a partition of this intervall.

b) Let f(x) =ln x on the intervall [1, 2] and let Pn be the partition Pn = {1, n+1 n , n+2 n , . . . , 2n−1 n , 2} where n ≥ 1 is an integer number. Find U(f, Pn) and L(f, Pn) and show that U(f, Pn) − L(f, Pn) = ln 2/nfor all n ≥ 1.


I have answered the a) assignement. but got stuck there. Can anyone help me?

 

[stapel]

a) Give the definition of upper and lower Riemann sums U(f, P) og L(f, P), where f is a limited function on an intervall [a, b] and P is a partition of this intervall.

b) Let f(x) =ln x on the intervall [1, 2] and let Pn be the partition Pn = {1, n+1 n , n+2 n , . . . , 2n−1 n , 2} where n ≥ 1 is an integer number. Find U(f, Pn) and L(f, Pn) and show that U(f, Pn) − L(f, Pn) = ln 2/nfor all n ≥ 1.

I have answered the a) assignement. but got stuck there. Can anyone help me?

They gave you definitions for the upper and lower sums. How far have you gotten in plugging the given function and given partition into the formulaic set-up they gave you?

Please be complete, so we can see where you're getting stuck. Thank you!