Réitigh 100(1-1/101^5)+100/101

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

Luacháil

$$\frac{1061416090100}{10510100501}\approx 100.990099$$

Céimeanna Réitigh

Ríomh cumhacht 101 de 5 agus faigh 10510100501.

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

Coinbhéartaigh 1 i gcodán \frac{10510100501}{10510100501}.

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

Tá an t-ainmneoir céanna ag \frac{10510100501}{10510100501} agus \frac{1}{10510100501} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

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

Dealaigh 1 ó 10510100501 chun 10510100500 a fháil.

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

Scríobh 100\times \frac{10510100500}{10510100501} mar chodán aonair.

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

Méadaigh 100 agus 10510100500 chun 1051010050000 a fháil.

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

Is é an t-iolrach is lú coitianta de 10510100501 agus 101 ná 10510100501. Coinbhéartaigh \frac{1051010050000}{10510100501} agus \frac{100}{101} chuig codáin a bhfuil an t-ainmneoir 10510100501 acu.

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

Tá an t-ainmneoir céanna ag \frac{1051010050000}{10510100501} agus \frac{10406040100}{10510100501} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

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

Suimigh 1051010050000 agus 10406040100 chun 1061416090100 a fháil.

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

Fachtóirigh

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 2549 \cdot 4164049}{101 ^ {5}} = 100\frac{10406040000}{10510100501} = 100.99009900038634$$