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

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

Aromātai

$$100$$

Ngā Upane Otinga

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

$$100\left(1-\frac{1}{1.0510100501}\right)+\frac{100}{1.01^{5}}$$

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

$$100\left(1-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01^{5}}$$

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

$$100\left(\frac{10510100501}{10510100501}-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01^{5}}$$

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.

$$100\times \frac{10510100501-10000000000}{10510100501}+\frac{100}{1.01^{5}}$$

Tangohia te 10000000000 i te 10510100501, ka 510100501.

$$100\times \frac{510100501}{10510100501}+\frac{100}{1.01^{5}}$$

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

$$\frac{100\times 510100501}{10510100501}+\frac{100}{1.01^{5}}$$

Whakareatia te 100 ki te 510100501, ka 51010050100.

$$\frac{51010050100}{10510100501}+\frac{100}{1.01^{5}}$$

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

$$\frac{51010050100}{10510100501}+\frac{100}{1.0510100501}$$

Whakarohaina te \frac{100}{1.0510100501} mā te whakarea i te taurunga me te tauraro ki te 10000000000.

$$\frac{51010050100}{10510100501}+\frac{1000000000000}{10510100501}$$

Tā te mea he rite te tauraro o \frac{51010050100}{10510100501} me \frac{1000000000000}{10510100501}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{51010050100+1000000000000}{10510100501}$$

Tāpirihia te 51010050100 ki te 1000000000000, ka 1051010050100.

$$\frac{1051010050100}{10510100501}$$

Whakawehea te 1051010050100 ki te 10510100501, kia riro ko 100.

$$100$$

Tauwehe

$$2^{2}\times 5^{2}$$