Whakaoti i te a_{n}=2n+1/n+2

$$a _ { n } = \frac { 2 n + 1 } { n + 2 }$$

Whakaoti mō n

$$n=-\frac{2a_{n}-1}{a_{n}-2}$$

$$a_{n}\neq 2$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe n ki -2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te n+2.

$$a_{n}\left(n+2\right)=2n+1$$

Whakamahia te āhuatanga tohatoha hei whakarea te a_{n} ki te n+2.

$$a_{n}n+2a_{n}=2n+1$$

Tangohia te 2n mai i ngā taha e rua.

$$a_{n}n+2a_{n}-2n=1$$

Tangohia te 2a_{n} mai i ngā taha e rua.

$$a_{n}n-2n=1-2a_{n}$$

Pahekotia ngā kīanga tau katoa e whai ana i te n.

$$\left(a_{n}-2\right)n=1-2a_{n}$$

Whakawehea ngā taha e rua ki te a_{n}-2.

$$\frac{\left(a_{n}-2\right)n}{a_{n}-2}=\frac{1-2a_{n}}{a_{n}-2}$$

Mā te whakawehe ki te a_{n}-2 ka wetekia te whakareanga ki te a_{n}-2.

$$n=\frac{1-2a_{n}}{a_{n}-2}$$

Tē taea kia ōrite te tāupe n ki -2.

$$n=\frac{1-2a_{n}}{a_{n}-2}\text{, }n\neq -2$$

Whakaoti mō a_n

$$a_{n}=\frac{2n+1}{n+2}$$

$$n\neq -2$$