Question Number 66803 by Rio Michael last updated on 19/Aug/19
$$\:{prove}\:{that} \\ $$$$\underset{{r}={k}} {\overset{{n}} {\sum}}\:{r}\:=\:\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right) \\ $$$$ \\ $$$${show}\:{with}\:{a}\:{diagram}\:{that}\:{the}\:{volume}\:{of}\:{a}\:{parallepipe}\:{is}\:\:\:{a}.\left({b}×{c}\right) \\ $$
Commented by JDamian last updated on 19/Aug/19
$${Did}\:{you}\:{mean}\:“{r}=\mathrm{1}''? \\ $$
Commented by Rio Michael last updated on 20/Aug/19
$${yes} \\ $$
Commented by Cmr 237 last updated on 20/Aug/19
$${vraiment} \\ $$
Answered by $@ty@m123 last updated on 20/Aug/19
![S=1+2+3+.....+n a=1, d=1 S=(n/2)[2a+(n−1)d] S=(n/2)[2+n−1] S=(1/2)n(n+1)](https://www.tinkutara.com/question/Q66838.png)
$${S}=\mathrm{1}+\mathrm{2}+\mathrm{3}+…..+{n} \\ $$$${a}=\mathrm{1},\:{d}=\mathrm{1} \\ $$$${S}=\frac{{n}}{\mathrm{2}}\left[\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right] \\ $$$${S}=\frac{{n}}{\mathrm{2}}\left[\mathrm{2}+{n}−\mathrm{1}\right] \\ $$$${S}=\frac{\mathrm{1}}{\mathrm{2}}{n}\left({n}+\mathrm{1}\right) \\ $$