2+5+8+...+3n-1=n(3n+1)/2

Giải thích các bước giải:

      $P=2+5+8+...+3n-1$

$\rightarrow P=(3.1-1)+(3.2-1)+(3.3-1)+..+(3.n-1)$

$\rightarrow P=3(1+2+3+...+n)-(1+1+..+1)\text{(n số 1)}$

$\rightarrow P=3\dfrac{n(n+1)}{2}-n$

$\rightarrow P=\dfrac{n(3n+1)}{2}$

`P` `=` `2` `+` `5` `+` `8` `+` `...` `+` `3n` `-` `1` 

`P` `=` `(` `3` `×` `1` `-` `1` `)` `+` `(` `3` `×` `2` `-` `1` `)` `+` `(` `3` `×` `3` `-` `1` `)` `+` `....` `(` `3` `×` `n` `-` `1` `)`

`P` `=` `3` `(` `1` `+` `2` `+` `3` `+` `...` `+` `n` `)` `-` `(` `1` `+` `1` `+` `...` `+` `1` `)` `(` `n_1` `)`

`P` `=` `3` $\dfrac{n ( n + 1 )}{2}$  `-` `n`

`P` `=` $\dfrac{n ( 3n + 1 )}{2}$  

$#Shawn$