Whakaoti i te 100(1-1/1.01^5)+100/1.01

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

Aromātai

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

Ngā Upane Otinga

Tātaihia te 1.01 mā te pū o 5, kia riro ko 1.0510100501.

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

Whakarohaina te \frac{1}{1.0510100501} mā te whakarea i te taurunga me te tauraro ki te 10000000000.

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

Me tahuri te 1 ki te hautau \frac{10510100501}{10510100501}.

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

Tā te mea he rite te tauraro o \frac{10510100501}{10510100501} me \frac{10000000000}{10510100501}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 10000000000 i te 10510100501, ka 510100501.

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

Tuhia te 100\times \frac{510100501}{10510100501} hei hautanga kotahi.

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

Whakareatia te 100 ki te 510100501, ka 51010050100.

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

Whakarohaina te \frac{100}{1.01} mā te whakarea i te taurunga me te tauraro ki te 100.

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

Ko te maha noa iti rawa atu o 10510100501 me 101 ko 10510100501. Me tahuri \frac{51010050100}{10510100501} me \frac{10000}{101} ki te hautau me te tautūnga 10510100501.

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

Tā te mea he rite te tauraro o \frac{51010050100}{10510100501} me \frac{1040604010000}{10510100501}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 51010050100 ki te 1040604010000, ka 1091614060100.

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

Tauwehe

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