Réitigh 100(1-1/1.01^5)+100/1.01

$$100 ( 1 - \frac { 1 } { 1.01 ^ { 5 } } ) + \frac { 100 } { 1.01 }$$

Luacháil

$$\frac{1091614060100}{10510100501}\approx 103.863332229$$

Céimeanna Réitigh

Ríomh cumhacht 1.01 de 5 agus faigh 1.0510100501.

$$100\left(1-\frac{1}{1.0510100501}\right)+\frac{100}{1.01}$$

Fairsingigh \frac{1}{1.0510100501} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 10000000000.

$$100\left(1-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01}$$

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

$$100\left(\frac{10510100501}{10510100501}-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01}$$

Tá an t-ainmneoir céanna ag \frac{10510100501}{10510100501} agus \frac{10000000000}{10510100501} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$100\times \frac{10510100501-10000000000}{10510100501}+\frac{100}{1.01}$$

Dealaigh 10000000000 ó 10510100501 chun 510100501 a fháil.

$$100\times \frac{510100501}{10510100501}+\frac{100}{1.01}$$

Scríobh 100\times \frac{510100501}{10510100501} mar chodán aonair.

$$\frac{100\times 510100501}{10510100501}+\frac{100}{1.01}$$

Méadaigh 100 agus 510100501 chun 51010050100 a fháil.

$$\frac{51010050100}{10510100501}+\frac{100}{1.01}$$

Fairsingigh \frac{100}{1.01} tríd an t-uimhreoir agus an t-ainmneoir araon a iolrú faoi 100.

$$\frac{51010050100}{10510100501}+\frac{10000}{101}$$

Is é an t-iolrach is lú coitianta de 10510100501 agus 101 ná 10510100501. Coinbhéartaigh \frac{51010050100}{10510100501} agus \frac{10000}{101} chuig codáin a bhfuil an t-ainmneoir 10510100501 acu.

$$\frac{51010050100}{10510100501}+\frac{1040604010000}{10510100501}$$

Tá an t-ainmneoir céanna ag \frac{51010050100}{10510100501} agus \frac{1040604010000}{10510100501} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{51010050100+1040604010000}{10510100501}$$

Suimigh 51010050100 agus 1040604010000 chun 1091614060100 a fháil.

$$\frac{1091614060100}{10510100501}$$

Fachtóirigh

$$\frac{53 \cdot 127 \cdot 1621771 \cdot 2 ^ {2} \cdot 5 ^ {2}}{101 ^ {5}} = 103\frac{9073708497}{10510100501} = 103.86333222942413$$