1/2^2+1/3^2+1/4^2 eching

$$\frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 3 ^ { 2 } } + \frac { 1 } { 4 ^ { 2 } }$$

Baholash

$$\frac{61}{144}\approx 0,423611111$$

Yechim qadamlari

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$\frac{1}{4}+\frac{1}{3^{2}}+\frac{1}{4^{2}}$$

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

$$\frac{1}{4}+\frac{1}{9}+\frac{1}{4^{2}}$$

4 va 9 ning eng kichik umumiy karralisi 36 ga teng. \frac{1}{4} va \frac{1}{9} ni 36 maxraj bilan kasrlarga aylantirib oling.

$$\frac{9}{36}+\frac{4}{36}+\frac{1}{4^{2}}$$

\frac{9}{36} va \frac{4}{36} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{9+4}{36}+\frac{1}{4^{2}}$$

13 olish uchun 9 va 4'ni qo'shing.

$$\frac{13}{36}+\frac{1}{4^{2}}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\frac{13}{36}+\frac{1}{16}$$

36 va 16 ning eng kichik umumiy karralisi 144 ga teng. \frac{13}{36} va \frac{1}{16} ni 144 maxraj bilan kasrlarga aylantirib oling.

$$\frac{52}{144}+\frac{9}{144}$$

\frac{52}{144} va \frac{9}{144} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{52+9}{144}$$

61 olish uchun 52 va 9'ni qo'shing.

$$\frac{61}{144}$$

Omil

$$\frac{61}{2 ^ {4} \cdot 3 ^ {2}} = 0,4236111111111111$$