100(1-1/101^5)+100/101 eching

$$100 ( 1 - \frac { 1 } { 101 ^ { 5 } } ) + \frac { 100 } { 101 }$$

Baholash

$$\frac{1061416090100}{10510100501}\approx 100,990099$$

Yechim qadamlari

5 daraja ko‘rsatkichini 101 ga hisoblang va 10510100501 ni qiymatni oling.

$$100\left(1-\frac{1}{10510100501}\right)+\frac{100}{101}$$

1 ni \frac{10510100501}{10510100501} kasrga o‘giring.

$$100\left(\frac{10510100501}{10510100501}-\frac{1}{10510100501}\right)+\frac{100}{101}$$

\frac{10510100501}{10510100501} va \frac{1}{10510100501} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$100\times \frac{10510100501-1}{10510100501}+\frac{100}{101}$$

10510100500 olish uchun 10510100501 dan 1 ni ayirish.

$$100\times \frac{10510100500}{10510100501}+\frac{100}{101}$$

100\times \frac{10510100500}{10510100501} ni yagona kasrga aylantiring.

$$\frac{100\times 10510100500}{10510100501}+\frac{100}{101}$$

1051010050000 hosil qilish uchun 100 va 10510100500 ni ko'paytirish.

$$\frac{1051010050000}{10510100501}+\frac{100}{101}$$

10510100501 va 101 ning eng kichik umumiy karralisi 10510100501 ga teng. \frac{1051010050000}{10510100501} va \frac{100}{101} ni 10510100501 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1051010050000}{10510100501}+\frac{10406040100}{10510100501}$$

\frac{1051010050000}{10510100501} va \frac{10406040100}{10510100501} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1051010050000+10406040100}{10510100501}$$

1061416090100 olish uchun 1051010050000 va 10406040100'ni qo'shing.

$$\frac{1061416090100}{10510100501}$$

Omil

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 2549 \cdot 4164049}{101 ^ {5}} = 100\frac{10406040000}{10510100501} = 100,99009900038634$$