Whakaoti i te 50(1-1/1.02^5)+100/1.02^5

$$50 ( 1 - \frac { 1 } { 1.02 ^ { 5 } } ) + \frac { 100 } { 1.02 ^ { 5 } }$$

Aromātai

$$\frac{32876262550}{345025251}\approx 95.286540491$$

Ngā Upane Otinga

Tātaihia te 1.02 mā te pū o 5, kia riro ko 1.1040808032.

$$50\left(1-\frac{1}{1.1040808032}\right)+\frac{100}{1.02^{5}}$$

Whakarohaina te \frac{1}{1.1040808032} mā te whakarea i te taurunga me te tauraro ki te 10000000000.

$$50\left(1-\frac{10000000000}{11040808032}\right)+\frac{100}{1.02^{5}}$$

Whakahekea te hautanga \frac{10000000000}{11040808032} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 32.

$$50\left(1-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Me tahuri te 1 ki te hautau \frac{345025251}{345025251}.

$$50\left(\frac{345025251}{345025251}-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Tā te mea he rite te tauraro o \frac{345025251}{345025251} me \frac{312500000}{345025251}, me tango rāua mā te tango i ō raua taurunga.

$$50\times \frac{345025251-312500000}{345025251}+\frac{100}{1.02^{5}}$$

Tangohia te 312500000 i te 345025251, ka 32525251.

$$50\times \frac{32525251}{345025251}+\frac{100}{1.02^{5}}$$

Tuhia te 50\times \frac{32525251}{345025251} hei hautanga kotahi.

$$\frac{50\times 32525251}{345025251}+\frac{100}{1.02^{5}}$$

Whakareatia te 50 ki te 32525251, ka 1626262550.

$$\frac{1626262550}{345025251}+\frac{100}{1.02^{5}}$$

Tātaihia te 1.02 mā te pū o 5, kia riro ko 1.1040808032.

$$\frac{1626262550}{345025251}+\frac{100}{1.1040808032}$$

Whakarohaina te \frac{100}{1.1040808032} mā te whakarea i te taurunga me te tauraro ki te 10000000000.

$$\frac{1626262550}{345025251}+\frac{1000000000000}{11040808032}$$

Whakahekea te hautanga \frac{1000000000000}{11040808032} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 32.

$$\frac{1626262550}{345025251}+\frac{31250000000}{345025251}$$

Tā te mea he rite te tauraro o \frac{1626262550}{345025251} me \frac{31250000000}{345025251}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1626262550+31250000000}{345025251}$$

Tāpirihia te 1626262550 ki te 31250000000, ka 32876262550.

$$\frac{32876262550}{345025251}$$

Tauwehe

$$\frac{2 \cdot 101 \cdot 6510151 \cdot 5 ^ {2}}{3 ^ {5} \cdot 17 ^ {5}} = 95\frac{98863705}{345025251} = 95.2865404914958$$