(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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).

2. Relevant 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].

3. 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.

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# Homework Help: Upper & Lower Partitions

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