- #1
Karol
- 1,380
- 22
Homework Statement
Homework Equations
Summs:
$$1+2+3+...+n=\frac{n(n+1)}{2}$$
$$1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$$
The Attempt at a Solution
$$\Delta x=\frac{b}{n}$$
$$S_n=f\left( \frac{\Delta x}{2} \right)\Delta x+f\left( \Delta x+\frac{\Delta x}{2} \right)\Delta x+...+f\left( (n-1)\Delta x+\frac{\Delta x}{2} \right)\Delta x$$
$$S_n=\left( \frac{b}{2n} \right) \frac{b}{n}+\left( \frac{b}{n}+\frac{b}{2n} \right) \frac{b}{n}+\left( 2\frac{b}{n}+\frac{b}{2n} \right) \frac{b}{n}+...+\left( (n-1)\frac{b}{n}+\frac{b}{2n} \right) \frac{b}{n}$$
$$S_n=\frac{b^2}{2n^2}(1+3+5+...+2n-1)$$
But i was taught, in that chapter, only the two sums from the Relevant Equations