b_{n}=n/n+1 eching

$$b _ { n } = \frac { n } { n + 1 }$$

n uchun yechish

$$n=-\frac{b_{n}}{b_{n}-1}$$

$$b_{n}\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

n qiymati -1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini n+1 ga ko'paytirish.

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

b_{n} ga n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$b_{n}n+b_{n}=n$$

Ikkala tarafdan n ni ayirish.

$$b_{n}n+b_{n}-n=0$$

Ikkala tarafdan b_{n} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$b_{n}n-n=-b_{n}$$

n'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini b_{n}-1 ga bo‘ling.

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

b_{n}-1 ga bo'lish b_{n}-1 ga ko'paytirishni bekor qiladi.

$$n=-\frac{b_{n}}{b_{n}-1}$$

n qiymati -1 teng bo‘lmaydi.

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

b_n uchun yechish

$$b_{n}=\frac{n}{n+1}$$

$$n\neq -1$$