a_{n}=2n+1/n+2 eching

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

n uchun yechish

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

$$a_{n}\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

n qiymati -2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n+2 ga ko'paytirish.

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

a_{n} ga n+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikkala tarafdan 2n ni ayirish.

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

Ikkala tarafdan 2a_{n} ni ayirish.

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

n'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini a_{n}-2 ga bo‘ling.

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

a_{n}-2 ga bo'lish a_{n}-2 ga ko'paytirishni bekor qiladi.

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

n qiymati -2 teng bo‘lmaydi.

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

a_n uchun yechish

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

$$n\neq -2$$