=(1+1/3)(1+1/5)(1+1/7)(1+1/9)(1+frac{1}{11}) eching

$$= ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 5 } ) ( 1 + \frac { 1 } { 7 } ) ( 1 + \frac { 1 } { 9 } ) ( 1 + \frac { 1 } { 11 } )$$

Baholash

$$\frac{512}{231}\approx 2,216450216$$

Yechim qadamlari

1 ni \frac{3}{3} kasrga o‘giring.

$$\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{3}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3+1}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

4 olish uchun 3 va 1'ni qo'shing.

$$\frac{4}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

1 ni \frac{5}{5} kasrga o‘giring.

$$\frac{4}{3}\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{5}{5} va \frac{1}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4}{3}\times \frac{5+1}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

6 olish uchun 5 va 1'ni qo'shing.

$$\frac{4}{3}\times \frac{6}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{6}{5} ga ko‘paytiring.

$$\frac{4\times 6}{3\times 5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{4\times 6}{3\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{24}{15}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{24}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{8}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

1 ni \frac{7}{7} kasrga o‘giring.

$$\frac{8}{5}\left(\frac{7}{7}+\frac{1}{7}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{7}{7} va \frac{1}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8}{5}\times \frac{7+1}{7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

8 olish uchun 7 va 1'ni qo'shing.

$$\frac{8}{5}\times \frac{8}{7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{5} ni \frac{8}{7} ga ko‘paytiring.

$$\frac{8\times 8}{5\times 7}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{8\times 8}{5\times 7} kasridagi ko‘paytirishlarni bajaring.

$$\frac{64}{35}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

1 ni \frac{9}{9} kasrga o‘giring.

$$\frac{64}{35}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{11}\right)$$

\frac{9}{9} va \frac{1}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{64}{35}\times \frac{9+1}{9}\left(1+\frac{1}{11}\right)$$

10 olish uchun 9 va 1'ni qo'shing.

$$\frac{64}{35}\times \frac{10}{9}\left(1+\frac{1}{11}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{64}{35} ni \frac{10}{9} ga ko‘paytiring.

$$\frac{64\times 10}{35\times 9}\left(1+\frac{1}{11}\right)$$

\frac{64\times 10}{35\times 9} kasridagi ko‘paytirishlarni bajaring.

$$\frac{640}{315}\left(1+\frac{1}{11}\right)$$

\frac{640}{315} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{128}{63}\left(1+\frac{1}{11}\right)$$

1 ni \frac{11}{11} kasrga o‘giring.

$$\frac{128}{63}\left(\frac{11}{11}+\frac{1}{11}\right)$$

\frac{11}{11} va \frac{1}{11} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{128}{63}\times \frac{11+1}{11}$$

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

$$\frac{128}{63}\times \frac{12}{11}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{128}{63} ni \frac{12}{11} ga ko‘paytiring.

$$\frac{128\times 12}{63\times 11}$$

\frac{128\times 12}{63\times 11} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1536}{693}$$

\frac{1536}{693} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{512}{231}$$

Omil

$$\frac{2 ^ {9}}{3 \cdot 7 \cdot 11} = 2\frac{50}{231} = 2,2164502164502164$$