Whakaoti i te {l}{1+1/2+1/3+1/4-1/5+frac{1}{6}}{+frac{1}{7}+frac{1}{8}+frac{1}{9}+frac{1}{10}+frac{1}{11}}{+frac{1}{12}+frac{1}{13}+frac{1}{14}+frac{1}{15}+frac{1}{16}}

$$\left. \begin{array} { l } { 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 5 } + \frac { 1 } { 6 } } \\ { + \frac { 1 } { 7 } + \frac { 1 } { 8 } + \frac { 1 } { 9 } + \frac { 1 } { 10 } + \frac { 1 } { 11 } } \\ { + \frac { 1 } { 12 } + \frac { 1 } { 13 } + \frac { 1 } { 14 } + \frac { 1 } { 15 } + \frac { 1 } { 16 } } \end{array} \right.$$

Aromātai

$$\frac{2148271}{720720}\approx 2.980728993$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{2}{2} me \frac{1}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2+1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{3}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{3}{2} me \frac{1}{3} ki te hautau me te tautūnga 6.

$$\frac{9}{6}+\frac{2}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{9}{6} me \frac{2}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{9+2}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 9 ki te 2, ka 11.

$$\frac{11}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 6 me 4 ko 12. Me tahuri \frac{11}{6} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$\frac{22}{12}+\frac{3}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{22}{12} me \frac{3}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{22+3}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 22 ki te 3, ka 25.

$$\frac{25}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 12 me 5 ko 60. Me tahuri \frac{25}{12} me \frac{1}{5} ki te hautau me te tautūnga 60.

$$\frac{125}{60}-\frac{12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{125}{60} me \frac{12}{60}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{125-12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tangohia te 12 i te 125, ka 113.

$$\frac{113}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 60 me 6 ko 60. Me tahuri \frac{113}{60} me \frac{1}{6} ki te hautau me te tautūnga 60.

$$\frac{113}{60}+\frac{10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{113}{60} me \frac{10}{60}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{113+10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 113 ki te 10, ka 123.

$$\frac{123}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Whakahekea te hautanga \frac{123}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{41}{20}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 20 me 7 ko 140. Me tahuri \frac{41}{20} me \frac{1}{7} ki te hautau me te tautūnga 140.

$$\frac{287}{140}+\frac{20}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{287}{140} me \frac{20}{140}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{287+20}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 287 ki te 20, ka 307.

$$\frac{307}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 140 me 8 ko 280. Me tahuri \frac{307}{140} me \frac{1}{8} ki te hautau me te tautūnga 280.

$$\frac{614}{280}+\frac{35}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{614}{280} me \frac{35}{280}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{614+35}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 614 ki te 35, ka 649.

$$\frac{649}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 280 me 9 ko 2520. Me tahuri \frac{649}{280} me \frac{1}{9} ki te hautau me te tautūnga 2520.

$$\frac{5841}{2520}+\frac{280}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{5841}{2520} me \frac{280}{2520}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5841+280}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 5841 ki te 280, ka 6121.

$$\frac{6121}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 2520 me 10 ko 2520. Me tahuri \frac{6121}{2520} me \frac{1}{10} ki te hautau me te tautūnga 2520.

$$\frac{6121}{2520}+\frac{252}{2520}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{6121}{2520} me \frac{252}{2520}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6121+252}{2520}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 6121 ki te 252, ka 6373.

$$\frac{6373}{2520}+\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 2520 me 11 ko 27720. Me tahuri \frac{6373}{2520} me \frac{1}{11} ki te hautau me te tautūnga 27720.

$$\frac{70103}{27720}+\frac{2520}{27720}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{70103}{27720} me \frac{2520}{27720}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{70103+2520}{27720}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 70103 ki te 2520, ka 72623.

$$\frac{72623}{27720}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 27720 me 12 ko 27720. Me tahuri \frac{72623}{27720} me \frac{1}{12} ki te hautau me te tautūnga 27720.

$$\frac{72623}{27720}+\frac{2310}{27720}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{72623}{27720} me \frac{2310}{27720}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{72623+2310}{27720}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 72623 ki te 2310, ka 74933.

$$\frac{74933}{27720}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 27720 me 13 ko 360360. Me tahuri \frac{74933}{27720} me \frac{1}{13} ki te hautau me te tautūnga 360360.

$$\frac{974129}{360360}+\frac{27720}{360360}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{974129}{360360} me \frac{27720}{360360}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{974129+27720}{360360}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 974129 ki te 27720, ka 1001849.

$$\frac{1001849}{360360}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 360360 me 14 ko 360360. Me tahuri \frac{1001849}{360360} me \frac{1}{14} ki te hautau me te tautūnga 360360.

$$\frac{1001849}{360360}+\frac{25740}{360360}+\frac{1}{15}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{1001849}{360360} me \frac{25740}{360360}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1001849+25740}{360360}+\frac{1}{15}+\frac{1}{16}$$

Tāpirihia te 1001849 ki te 25740, ka 1027589.

$$\frac{1027589}{360360}+\frac{1}{15}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 360360 me 15 ko 360360. Me tahuri \frac{1027589}{360360} me \frac{1}{15} ki te hautau me te tautūnga 360360.

$$\frac{1027589}{360360}+\frac{24024}{360360}+\frac{1}{16}$$

Tā te mea he rite te tauraro o \frac{1027589}{360360} me \frac{24024}{360360}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1027589+24024}{360360}+\frac{1}{16}$$

Tāpirihia te 1027589 ki te 24024, ka 1051613.

$$\frac{1051613}{360360}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 360360 me 16 ko 720720. Me tahuri \frac{1051613}{360360} me \frac{1}{16} ki te hautau me te tautūnga 720720.

$$\frac{2103226}{720720}+\frac{45045}{720720}$$

Tā te mea he rite te tauraro o \frac{2103226}{720720} me \frac{45045}{720720}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2103226+45045}{720720}$$

Tāpirihia te 2103226 ki te 45045, ka 2148271.

$$\frac{2148271}{720720}$$

Tauwehe

$$\frac{103 \cdot 20857}{2 ^ {4} \cdot 3 ^ {2} \cdot 5 \cdot 7 \cdot 11 \cdot 13} = 2\frac{706831}{720720} = 2.9807289932289933$$