Whakaoti i te 100(1-1/101^5)+100/101

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

Aromātai

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

Ngā Upane Otinga

Tātaihia te 101 mā te pū o 5, kia riro ko 10510100501.

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

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

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

Tā te mea he rite te tauraro o \frac{10510100501}{10510100501} me \frac{1}{10510100501}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 10510100501, ka 10510100500.

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

Tuhia te 100\times \frac{10510100500}{10510100501} hei hautanga kotahi.

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

Whakareatia te 100 ki te 10510100500, ka 1051010050000.

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

Ko te maha noa iti rawa atu o 10510100501 me 101 ko 10510100501. Me tahuri \frac{1051010050000}{10510100501} me \frac{100}{101} ki te hautau me te tautūnga 10510100501.

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

Tā te mea he rite te tauraro o \frac{1051010050000}{10510100501} me \frac{10406040100}{10510100501}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 1051010050000 ki te 10406040100, ka 1061416090100.

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

Tauwehe

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