256left({left(frac{1/2right)}^10-1right)}{1/2-1} eching

$$\frac{ 256 \left( { \left( \frac{ 1 }{ 2 } \right) }^{ 10 } -1 \right) }{ \frac{ 1 }{ 2 } -1 }$$

Baholash

$$\frac{1023}{2}=511,5$$

Yechim qadamlari

10 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{1024} ni qiymatni oling.

$$\frac{256\left(\frac{1}{1024}-1\right)}{\frac{1}{2}-1}$$

1 ni \frac{1024}{1024} kasrga o‘giring.

$$\frac{256\left(\frac{1}{1024}-\frac{1024}{1024}\right)}{\frac{1}{2}-1}$$

\frac{1}{1024} va \frac{1024}{1024} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{256\times \frac{1-1024}{1024}}{\frac{1}{2}-1}$$

-1023 olish uchun 1 dan 1024 ni ayirish.

$$\frac{256\left(-\frac{1023}{1024}\right)}{\frac{1}{2}-1}$$

256\left(-\frac{1023}{1024}\right) ni yagona kasrga aylantiring.

$$\frac{\frac{256\left(-1023\right)}{1024}}{\frac{1}{2}-1}$$

-261888 hosil qilish uchun 256 va -1023 ni ko'paytirish.

$$\frac{\frac{-261888}{1024}}{\frac{1}{2}-1}$$

\frac{-261888}{1024} ulushini 256 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{-\frac{1023}{4}}{\frac{1}{2}-1}$$

1 ni \frac{2}{2} kasrga o‘giring.

$$\frac{-\frac{1023}{4}}{\frac{1}{2}-\frac{2}{2}}$$

\frac{1}{2} va \frac{2}{2} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-\frac{1023}{4}}{\frac{1-2}{2}}$$

-1 olish uchun 1 dan 2 ni ayirish.

$$\frac{-\frac{1023}{4}}{-\frac{1}{2}}$$

-\frac{1023}{4} ni -\frac{1}{2} ga bo'lish -\frac{1023}{4} ga k'paytirish -\frac{1}{2} ga qaytarish.

$$-\frac{1023}{4}\left(-2\right)$$

-\frac{1023}{4}\left(-2\right) ni yagona kasrga aylantiring.

$$\frac{-1023\left(-2\right)}{4}$$

2046 hosil qilish uchun -1023 va -2 ni ko'paytirish.

$$\frac{2046}{4}$$

\frac{2046}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1023}{2}$$

Omil

$$\frac{3 \cdot 11 \cdot 31}{2} = 511\frac{1}{2} = 511,5$$