Whakaoti i te 1/2^2+1/3^2+1/4^2

$$\frac { 1 } { 2 ^ { 2 } } + \frac { 1 } { 3 ^ { 2 } } + \frac { 1 } { 4 ^ { 2 } }$$

Aromātai

$$\frac{61}{144}\approx 0.423611111$$

Ngā Upane Otinga

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{1}{4}+\frac{1}{3^{2}}+\frac{1}{4^{2}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\frac{1}{4}+\frac{1}{9}+\frac{1}{4^{2}}$$

Ko te maha noa iti rawa atu o 4 me 9 ko 36. Me tahuri \frac{1}{4} me \frac{1}{9} ki te hautau me te tautūnga 36.

$$\frac{9}{36}+\frac{4}{36}+\frac{1}{4^{2}}$$

Tā te mea he rite te tauraro o \frac{9}{36} me \frac{4}{36}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{9+4}{36}+\frac{1}{4^{2}}$$

Tāpirihia te 9 ki te 4, ka 13.

$$\frac{13}{36}+\frac{1}{4^{2}}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$\frac{13}{36}+\frac{1}{16}$$

Ko te maha noa iti rawa atu o 36 me 16 ko 144. Me tahuri \frac{13}{36} me \frac{1}{16} ki te hautau me te tautūnga 144.

$$\frac{52}{144}+\frac{9}{144}$$

Tā te mea he rite te tauraro o \frac{52}{144} me \frac{9}{144}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{52+9}{144}$$

Tāpirihia te 52 ki te 9, ka 61.

$$\frac{61}{144}$$

Tauwehe

$$\frac{61}{2 ^ {4} \cdot 3 ^ {2}} = 0.4236111111111111$$