- #1
Youngster
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Homework Statement
I'm actually asked to calculate the area under the curve 5x + x2 over the interval [0,1] using Riemann Sums. I found the formula for the Riemann sum over the interval, it being the following:
[itex]\sum[/itex][itex]^{n}_{k=1}[/itex] ([itex]\frac{5k}{n}[/itex]+[itex]\frac{k^{2}}{n^{2}}[/itex])([itex]\frac{1}{n}[/itex])
However, I am asked to simplify the sigma notation to find the sum in terms of n only, which is where I'm currently stuck.
Homework Equations
None, I believe. Except perhaps the sum formulas for positive integers
The Attempt at a Solution
I actually just went ahead and multiplied through and separated each term like so
[itex]\frac{5}{n^{2}}[/itex][itex]\sum[/itex][itex]^{n}_{k=1}[/itex] k +[itex]\frac{1}{n^{3}}[/itex][itex]\sum[/itex][itex]^{n}_{k=1}[/itex] k[itex]^{2}[/itex]
I, however, was left with something completely different from the expected answers given. Am I going through this correctly?