Evaluate 1/6+1/18+1/54+1/162+1/486

$\frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Step 1

Find the common denominator.

Multiply $\frac{1}{6}$ by $\frac{81}{81}$ .

$\frac{1}{6} \cdot \frac{81}{81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{6}$ by $\frac{81}{81}$ .

$\frac{81}{6 \cdot 81} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{18}$ by $\frac{27}{27}$ .

$\frac{81}{6 \cdot 81} + \frac{1}{18} \cdot \frac{27}{27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{18}$ by $\frac{27}{27}$ .

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{54}$ by $\frac{9}{9}$ .

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{1}{54} \cdot \frac{9}{9} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{54}$ by $\frac{9}{9}$ .

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} + \frac{1}{486}$

Multiply $\frac{1}{162}$ by $\frac{3}{3}$ .

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{1}{162} \cdot \frac{3}{3} + \frac{1}{486}$

Multiply $\frac{1}{162}$ by $\frac{3}{3}$ .

$\frac{81}{6 \cdot 81} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Multiply $6$ by $81$ .

$\frac{81}{486} + \frac{27}{18 \cdot 27} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Multiply $18$ by $27$ .

$\frac{81}{486} + \frac{27}{486} + \frac{9}{54 \cdot 9} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Reorder the factors of $54 \cdot 9$ .

$\frac{81}{486} + \frac{27}{486} + \frac{9}{9 \cdot 54} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Multiply $9$ by $54$ .

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{162 \cdot 3} + \frac{1}{486}$

Reorder the factors of $162 \cdot 3$ .

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{3 \cdot 162} + \frac{1}{486}$

Multiply $3$ by $162$ .

$\frac{81}{486} + \frac{27}{486} + \frac{9}{486} + \frac{3}{486} + \frac{1}{486}$

Step 2

Combine the numerators over the common denominator.

$\frac{81 + 27 + 9 + 3 + 1}{486}$

Step 3

Simplify by adding numbers.

Add $81$ and $27$ .

$\frac{108 + 9 + 3 + 1}{486}$

Add $108$ and $9$ .

$\frac{117 + 3 + 1}{486}$

Add $117$ and $3$ .

$\frac{120 + 1}{486}$

Add $120$ and $1$ .

$\frac{121}{486}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{121}{486}$

Decimal Form:

$0.24897119 \dots$

Evaluate 1/6+1/18+1/54+1/162+1/486

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