left(1+1/3right)left(1+1/3^2right)left(1+1/3^4right) eching

$$\left( 1+ \frac{ 1 }{ 3 } \right) \left( 1+ \frac{ 1 }{ { 3 }^{ 2 } } \right) \left( 1+ \frac{ 1 }{ { 3 }^{ 4 } } \right)$$

Baholash

$$\frac{3280}{2187}\approx 1,499771376$$

Yechim qadamlari

1 ni \frac{3}{3} kasrga o‘giring.

$$\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

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

$$\frac{3+1}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

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

$$\frac{4}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{4}{3}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)$$

1 ni \frac{9}{9} kasrga o‘giring.

$$\frac{4}{3}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)$$

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

$$\frac{4}{3}\times \frac{9+1}{9}\left(1+\frac{1}{3^{4}}\right)$$

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

$$\frac{4}{3}\times \frac{10}{9}\left(1+\frac{1}{3^{4}}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{10}{9} ga ko‘paytiring.

$$\frac{4\times 10}{3\times 9}\left(1+\frac{1}{3^{4}}\right)$$

\frac{4\times 10}{3\times 9} kasridagi ko‘paytirishlarni bajaring.

$$\frac{40}{27}\left(1+\frac{1}{3^{4}}\right)$$

4 daraja ko‘rsatkichini 3 ga hisoblang va 81 ni qiymatni oling.

$$\frac{40}{27}\left(1+\frac{1}{81}\right)$$

1 ni \frac{81}{81} kasrga o‘giring.

$$\frac{40}{27}\left(\frac{81}{81}+\frac{1}{81}\right)$$

\frac{81}{81} va \frac{1}{81} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{40}{27}\times \frac{81+1}{81}$$

82 olish uchun 81 va 1'ni qo'shing.

$$\frac{40}{27}\times \frac{82}{81}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{40}{27} ni \frac{82}{81} ga ko‘paytiring.

$$\frac{40\times 82}{27\times 81}$$

\frac{40\times 82}{27\times 81} kasridagi ko‘paytirishlarni bajaring.

$$\frac{3280}{2187}$$

Omil

$$\frac{2 ^ {4} \cdot 5 \cdot 41}{3 ^ {7}} = 1\frac{1093}{2187} = 1,4997713763145861$$