1/9!+1/10!+1/11!=122/11! eching

$$\frac { 1 } { 9 ! } + \frac { 1 } { 10 ! } + \frac { 1 } { 11 ! } = \frac { 122 } { 11 ! }$$

Tasdiqlamoq

Yechim qadamlari

9 ning faktoriali 362880 ga teng.

$$\frac{1}{362880}+\frac{1}{10!}+\frac{1}{11!}=\frac{122}{11!}$$

10 ning faktoriali 3628800 ga teng.

$$\frac{1}{362880}+\frac{1}{3628800}+\frac{1}{11!}=\frac{122}{11!}$$

362880 va 3628800 ning eng kichik umumiy karralisi 3628800 ga teng. \frac{1}{362880} va \frac{1}{3628800} ni 3628800 maxraj bilan kasrlarga aylantirib oling.

$$\frac{10}{3628800}+\frac{1}{3628800}+\frac{1}{11!}=\frac{122}{11!}$$

\frac{10}{3628800} va \frac{1}{3628800} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{10+1}{3628800}+\frac{1}{11!}=\frac{122}{11!}$$

11 olish uchun 10 va 1'ni qo'shing.

$$\frac{11}{3628800}+\frac{1}{11!}=\frac{122}{11!}$$

11 ning faktoriali 39916800 ga teng.

$$\frac{11}{3628800}+\frac{1}{39916800}=\frac{122}{11!}$$

3628800 va 39916800 ning eng kichik umumiy karralisi 39916800 ga teng. \frac{11}{3628800} va \frac{1}{39916800} ni 39916800 maxraj bilan kasrlarga aylantirib oling.

$$\frac{121}{39916800}+\frac{1}{39916800}=\frac{122}{11!}$$

\frac{121}{39916800} va \frac{1}{39916800} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{121+1}{39916800}=\frac{122}{11!}$$

122 olish uchun 121 va 1'ni qo'shing.

$$\frac{122}{39916800}=\frac{122}{11!}$$

\frac{122}{39916800} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{61}{19958400}=\frac{122}{11!}$$

11 ning faktoriali 39916800 ga teng.

$$\frac{61}{19958400}=\frac{122}{39916800}$$

\frac{122}{39916800} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{61}{19958400}=\frac{61}{19958400}$$

\frac{61}{19958400} va \frac{61}{19958400} ni taqqoslang.

$$\text{true}$$