1div2^11+1div2^12+1div2^13+1div2^14+1div{2}^15+1div{2}^16 eching

$$1 \div { 2 }^{ 11 } +1 \div { 2 }^{ 12 } +1 \div { 2 }^{ 13 } +1 \div { 2 }^{ 14 } +1 \div { 2 }^{ 15 } +1 \div { 2 }^{ 16 }$$

Baholash

$$\frac{63}{65536}=0,000961304$$

Yechim qadamlari

11 daraja ko‘rsatkichini 2 ga hisoblang va 2048 ni qiymatni oling.

$$\frac{1}{2048}+\frac{1}{2^{12}}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

12 daraja ko‘rsatkichini 2 ga hisoblang va 4096 ni qiymatni oling.

$$\frac{1}{2048}+\frac{1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

2048 va 4096 ning eng kichik umumiy karralisi 4096 ga teng. \frac{1}{2048} va \frac{1}{4096} ni 4096 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{4096}+\frac{1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

\frac{2}{4096} va \frac{1}{4096} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2+1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

3 olish uchun 2 va 1'ni qo'shing.

$$\frac{3}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

13 daraja ko‘rsatkichini 2 ga hisoblang va 8192 ni qiymatni oling.

$$\frac{3}{4096}+\frac{1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

4096 va 8192 ning eng kichik umumiy karralisi 8192 ga teng. \frac{3}{4096} va \frac{1}{8192} ni 8192 maxraj bilan kasrlarga aylantirib oling.

$$\frac{6}{8192}+\frac{1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

\frac{6}{8192} va \frac{1}{8192} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{6+1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

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

$$\frac{7}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

14 daraja ko‘rsatkichini 2 ga hisoblang va 16384 ni qiymatni oling.

$$\frac{7}{8192}+\frac{1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

8192 va 16384 ning eng kichik umumiy karralisi 16384 ga teng. \frac{7}{8192} va \frac{1}{16384} ni 16384 maxraj bilan kasrlarga aylantirib oling.

$$\frac{14}{16384}+\frac{1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

\frac{14}{16384} va \frac{1}{16384} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{14+1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

15 olish uchun 14 va 1'ni qo'shing.

$$\frac{15}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

15 daraja ko‘rsatkichini 2 ga hisoblang va 32768 ni qiymatni oling.

$$\frac{15}{16384}+\frac{1}{32768}+\frac{1}{2^{16}}$$

16384 va 32768 ning eng kichik umumiy karralisi 32768 ga teng. \frac{15}{16384} va \frac{1}{32768} ni 32768 maxraj bilan kasrlarga aylantirib oling.

$$\frac{30}{32768}+\frac{1}{32768}+\frac{1}{2^{16}}$$

\frac{30}{32768} va \frac{1}{32768} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{30+1}{32768}+\frac{1}{2^{16}}$$

31 olish uchun 30 va 1'ni qo'shing.

$$\frac{31}{32768}+\frac{1}{2^{16}}$$

16 daraja ko‘rsatkichini 2 ga hisoblang va 65536 ni qiymatni oling.

$$\frac{31}{32768}+\frac{1}{65536}$$

32768 va 65536 ning eng kichik umumiy karralisi 65536 ga teng. \frac{31}{32768} va \frac{1}{65536} ni 65536 maxraj bilan kasrlarga aylantirib oling.

$$\frac{62}{65536}+\frac{1}{65536}$$

\frac{62}{65536} va \frac{1}{65536} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{62+1}{65536}$$

63 olish uchun 62 va 1'ni qo'shing.

$$\frac{63}{65536}$$

Omil

$$\frac{3 ^ {2} \cdot 7}{2 ^ {16}} = 0,0009613037109375$$