$\displaystyle1+2+3+ ...+ n = \frac{n(n+1)}{2}\text{, where n is a positive integer}$
呢樣野我都知點證明
$\displaystyle1+2+3+...+n\text{, }n+(n-1)+...+1$
$\displaystyle2(1+2+3+...+n)=n(n+1)$
$\displaystyle1+2+3+ ...+ n = \frac{n(n+1)}{2}$

但係我想問$\displaystyle1^3+2^3+3^3+...+n^3=\frac{n^2(n+1)^2}{4}$
同埋呢啲$\forall x\neq0, \displaystyle \sum_{k=1}^n \sin kx=\displaystyle \frac{\sin(\frac{(n+1)x}{2})\sin(\frac{nx}{2})}{\sin(\frac{x}{2})}$
又係點搵出尼
其實係咪條條式都可以咁樣做？當中又有冇咩限制？
唔該