Whakaoti i te x=100/(109)^2+100/(109)^3+100/(109)^4+100/(109)^4

$$x = \frac { 100 } { ( 109 ) ^ { 2 } } + \frac { 100 } { ( 109 ) ^ { 3 } } + \frac { 100 } { ( 109 ) ^ { 4 } } + \frac { 100 } { ( 109 ) ^ { 4 } }$$

Whakaoti mō x

$$x=\frac{1199200}{141158161}\approx 0.008495435$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 109 mā te pū o 2, kia riro ko 11881.

$$x=\frac{100}{11881}+\frac{100}{109^{3}}+\frac{100}{109^{4}}+\frac{100}{109^{4}}$$

Tātaihia te 109 mā te pū o 3, kia riro ko 1295029.

$$x=\frac{100}{11881}+\frac{100}{1295029}+\frac{100}{109^{4}}+\frac{100}{109^{4}}$$

Ko te maha noa iti rawa atu o 11881 me 1295029 ko 1295029. Me tahuri \frac{100}{11881} me \frac{100}{1295029} ki te hautau me te tautūnga 1295029.

$$x=\frac{10900}{1295029}+\frac{100}{1295029}+\frac{100}{109^{4}}+\frac{100}{109^{4}}$$

Tā te mea he rite te tauraro o \frac{10900}{1295029} me \frac{100}{1295029}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{10900+100}{1295029}+\frac{100}{109^{4}}+\frac{100}{109^{4}}$$

Tāpirihia te 10900 ki te 100, ka 11000.

$$x=\frac{11000}{1295029}+\frac{100}{109^{4}}+\frac{100}{109^{4}}$$

Tātaihia te 109 mā te pū o 4, kia riro ko 141158161.

$$x=\frac{11000}{1295029}+\frac{100}{141158161}+\frac{100}{109^{4}}$$

Ko te maha noa iti rawa atu o 1295029 me 141158161 ko 141158161. Me tahuri \frac{11000}{1295029} me \frac{100}{141158161} ki te hautau me te tautūnga 141158161.

$$x=\frac{1199000}{141158161}+\frac{100}{141158161}+\frac{100}{109^{4}}$$

Tā te mea he rite te tauraro o \frac{1199000}{141158161} me \frac{100}{141158161}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{1199000+100}{141158161}+\frac{100}{109^{4}}$$

Tāpirihia te 1199000 ki te 100, ka 1199100.

$$x=\frac{1199100}{141158161}+\frac{100}{109^{4}}$$

Tātaihia te 109 mā te pū o 4, kia riro ko 141158161.

$$x=\frac{1199100}{141158161}+\frac{100}{141158161}$$

Tā te mea he rite te tauraro o \frac{1199100}{141158161} me \frac{100}{141158161}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$x=\frac{1199100+100}{141158161}$$

Tāpirihia te 1199100 ki te 100, ka 1199200.

$$x=\frac{1199200}{141158161}$$

Tautapa x

$$x≔\frac{1199200}{141158161}$$