Whakaoti i te (1/1*4+1/4*7+1/7*10+1/10*13+frac{1}{13*16})=

$$( \frac { 1 } { 1 \cdot 4 } + \frac { 1 } { 4 \cdot 7 } + \frac { 1 } { 7 \cdot 10 } + \frac { 1 } { 10 \cdot 13 } + \frac { 1 } { 13 \cdot 16 } ) =$$

Aromātai

$$\frac{5}{16}=0.3125$$

Ngā Upane Otinga

Whakareatia te 1 ki te 4, ka 4.

$$\frac{1}{4}+\frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Whakareatia te 4 ki te 7, ka 28.

$$\frac{1}{4}+\frac{1}{28}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Ko te maha noa iti rawa atu o 4 me 28 ko 28. Me tahuri \frac{1}{4} me \frac{1}{28} ki te hautau me te tautūnga 28.

$$\frac{7}{28}+\frac{1}{28}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Tā te mea he rite te tauraro o \frac{7}{28} me \frac{1}{28}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7+1}{28}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Tāpirihia te 7 ki te 1, ka 8.

$$\frac{8}{28}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Whakahekea te hautanga \frac{8}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{2}{7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Whakareatia te 7 ki te 10, ka 70.

$$\frac{2}{7}+\frac{1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Ko te maha noa iti rawa atu o 7 me 70 ko 70. Me tahuri \frac{2}{7} me \frac{1}{70} ki te hautau me te tautūnga 70.

$$\frac{20}{70}+\frac{1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Tā te mea he rite te tauraro o \frac{20}{70} me \frac{1}{70}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{20+1}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Tāpirihia te 20 ki te 1, ka 21.

$$\frac{21}{70}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Whakahekea te hautanga \frac{21}{70} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{3}{10}+\frac{1}{10\times 13}+\frac{1}{13\times 16}$$

Whakareatia te 10 ki te 13, ka 130.

$$\frac{3}{10}+\frac{1}{130}+\frac{1}{13\times 16}$$

Ko te maha noa iti rawa atu o 10 me 130 ko 130. Me tahuri \frac{3}{10} me \frac{1}{130} ki te hautau me te tautūnga 130.

$$\frac{39}{130}+\frac{1}{130}+\frac{1}{13\times 16}$$

Tā te mea he rite te tauraro o \frac{39}{130} me \frac{1}{130}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{39+1}{130}+\frac{1}{13\times 16}$$

Tāpirihia te 39 ki te 1, ka 40.

$$\frac{40}{130}+\frac{1}{13\times 16}$$

Whakahekea te hautanga \frac{40}{130} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{4}{13}+\frac{1}{13\times 16}$$

Whakareatia te 13 ki te 16, ka 208.

$$\frac{4}{13}+\frac{1}{208}$$

Ko te maha noa iti rawa atu o 13 me 208 ko 208. Me tahuri \frac{4}{13} me \frac{1}{208} ki te hautau me te tautūnga 208.

$$\frac{64}{208}+\frac{1}{208}$$

Tā te mea he rite te tauraro o \frac{64}{208} me \frac{1}{208}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{64+1}{208}$$

Tāpirihia te 64 ki te 1, ka 65.

$$\frac{65}{208}$$

Whakahekea te hautanga \frac{65}{208} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 13.

$$\frac{5}{16}$$

Tauwehe

$$\frac{5}{2 ^ {4}} = 0.3125$$