- #1
jdz86
- 21
- 0
Homework Statement
Let f(x) = x, x [tex]\in[/tex] [0,1], [tex]P_{n}[/tex] = {0, [tex]\frac{1}{n}[/tex], [tex]\frac{2}{n}[/tex],..., [tex]\frac{n}{n}[/tex] = 1}.
Calculate [tex]U_{P_{n}}[/tex](f) and [tex]L_{P_{n}}[/tex](f).
Homework Equations
[tex]U_{P_{n}}[/tex](f) is the sum of the upper partitions and [tex]L_{P_{n}}[/tex](f) is the sum of the lower partitions.
A hint was [tex]\sum^{n}_{k=1}[/tex] = [tex]\frac{n(n+1)}{2}[/tex].
The Attempt at a Solution
I know that:
[tex]U_{P_{n}}[/tex](f) = 1/2 + 1/2n
and
[tex]L_{P_{n}}[/tex](f) = 1/2 - 1/2n
just can't figure out how to get them.