Whakaoti i te 1div2^11+1div2^12+1div2^13+1div2^14+1div{2}^15+1div{2}^16

$$1 \div { 2 }^{ 11 } +1 \div { 2 }^{ 12 } +1 \div { 2 }^{ 13 } +1 \div { 2 }^{ 14 } +1 \div { 2 }^{ 15 } +1 \div { 2 }^{ 16 }$$

Aromātai

$$\frac{63}{65536}=0.000961304$$

Ngā Upane Otinga

Tātaihia te 2 mā te pū o 11, kia riro ko 2048.

$$\frac{1}{2048}+\frac{1}{2^{12}}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tātaihia te 2 mā te pū o 12, kia riro ko 4096.

$$\frac{1}{2048}+\frac{1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Ko te maha noa iti rawa atu o 2048 me 4096 ko 4096. Me tahuri \frac{1}{2048} me \frac{1}{4096} ki te hautau me te tautūnga 4096.

$$\frac{2}{4096}+\frac{1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tā te mea he rite te tauraro o \frac{2}{4096} me \frac{1}{4096}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2+1}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{3}{4096}+\frac{1}{2^{13}}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tātaihia te 2 mā te pū o 13, kia riro ko 8192.

$$\frac{3}{4096}+\frac{1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Ko te maha noa iti rawa atu o 4096 me 8192 ko 8192. Me tahuri \frac{3}{4096} me \frac{1}{8192} ki te hautau me te tautūnga 8192.

$$\frac{6}{8192}+\frac{1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tā te mea he rite te tauraro o \frac{6}{8192} me \frac{1}{8192}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6+1}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{7}{8192}+\frac{1}{2^{14}}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tātaihia te 2 mā te pū o 14, kia riro ko 16384.

$$\frac{7}{8192}+\frac{1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Ko te maha noa iti rawa atu o 8192 me 16384 ko 16384. Me tahuri \frac{7}{8192} me \frac{1}{16384} ki te hautau me te tautūnga 16384.

$$\frac{14}{16384}+\frac{1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tā te mea he rite te tauraro o \frac{14}{16384} me \frac{1}{16384}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{14+1}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tāpirihia te 14 ki te 1, ka 15.

$$\frac{15}{16384}+\frac{1}{2^{15}}+\frac{1}{2^{16}}$$

Tātaihia te 2 mā te pū o 15, kia riro ko 32768.

$$\frac{15}{16384}+\frac{1}{32768}+\frac{1}{2^{16}}$$

Ko te maha noa iti rawa atu o 16384 me 32768 ko 32768. Me tahuri \frac{15}{16384} me \frac{1}{32768} ki te hautau me te tautūnga 32768.

$$\frac{30}{32768}+\frac{1}{32768}+\frac{1}{2^{16}}$$

Tā te mea he rite te tauraro o \frac{30}{32768} me \frac{1}{32768}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{30+1}{32768}+\frac{1}{2^{16}}$$

Tāpirihia te 30 ki te 1, ka 31.

$$\frac{31}{32768}+\frac{1}{2^{16}}$$

Tātaihia te 2 mā te pū o 16, kia riro ko 65536.

$$\frac{31}{32768}+\frac{1}{65536}$$

Ko te maha noa iti rawa atu o 32768 me 65536 ko 65536. Me tahuri \frac{31}{32768} me \frac{1}{65536} ki te hautau me te tautūnga 65536.

$$\frac{62}{65536}+\frac{1}{65536}$$

Tā te mea he rite te tauraro o \frac{62}{65536} me \frac{1}{65536}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{62+1}{65536}$$

Tāpirihia te 62 ki te 1, ka 63.

$$\frac{63}{65536}$$

Tauwehe

$$\frac{3 ^ {2} \cdot 7}{2 ^ {16}} = 0.0009613037109375$$