Lahenda 100(1-1/101^5)+100/101

$$100 ( 1 - \frac { 1 } { 101 ^ { 5 } } ) + \frac { 100 } { 101 }$$

Arvuta

$$\frac{1061416090100}{10510100501}\approx 100,990099$$

Lahenduse etapid

Arvutage 5 aste 101 ja leidke 10510100501.

$$100\left(1-\frac{1}{10510100501}\right)+\frac{100}{101}$$

Teisendage 1 murdarvuks \frac{10510100501}{10510100501}.

$$100\left(\frac{10510100501}{10510100501}-\frac{1}{10510100501}\right)+\frac{100}{101}$$

Kuna murdudel \frac{10510100501}{10510100501} ja \frac{1}{10510100501} on sama nimetaja, lahutage nende lugejad.

$$100\times \frac{10510100501-1}{10510100501}+\frac{100}{101}$$

Lahutage 1 väärtusest 10510100501, et leida 10510100500.

$$100\times \frac{10510100500}{10510100501}+\frac{100}{101}$$

Avaldage 100\times \frac{10510100500}{10510100501} ühe murdarvuna.

$$\frac{100\times 10510100500}{10510100501}+\frac{100}{101}$$

Korrutage 100 ja 10510100500, et leida 1051010050000.

$$\frac{1051010050000}{10510100501}+\frac{100}{101}$$

10510100501 ja 101 vähim ühiskordne on 10510100501. Teisendage \frac{1051010050000}{10510100501} ja \frac{100}{101} murdarvudeks, mille nimetaja on 10510100501.

$$\frac{1051010050000}{10510100501}+\frac{10406040100}{10510100501}$$

Kuna murdudel \frac{1051010050000}{10510100501} ja \frac{10406040100}{10510100501} on sama nimetaja, liitke nende lugejad.

$$\frac{1051010050000+10406040100}{10510100501}$$

Liitke 1051010050000 ja 10406040100, et leida 1061416090100.

$$\frac{1061416090100}{10510100501}$$

Lahuta teguriteks

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 2549 \cdot 4164049}{101 ^ {5}} = 100\frac{10406040000}{10510100501} = 100,99009900038634$$