Question

find the sum of series 0.7+0.07+0.007+......​

Answer 1

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Answer 2

$\displaystyle \sf{ 0.7 + 0.07 + 0.007 + ... }= \frac{7}{9}$

Given :

$\displaystyle \sf{ 0.7 + 0.07 + 0.007 + ... }$

To find :

The sum

Formula :

Let a be the First term and r ( < 1 ) be the Common ratio

Then the sum of the Geometric Progression infinite

number of terms

$\displaystyle \sf = \frac{a}{1 - r}$

Solution :

Step 1 of 3 :

Write down the given progression

Here the given progression is

$\displaystyle \sf{ 0.7 + 0.07 + 0.007 + ... }$

This is a geometric progression with infinite number of terms

Step 2 of 3 :

Find first term and common ratio

First term = a = 0.7

Common Ratio = r = 0.07/0.7 = 0.1 < 1

Step 3 of 3 :

Find the sum

The geometric progression is with infinite number of terms

Hence the required sum

$\displaystyle \sf = \frac{a}{1 - r}$

$\displaystyle \sf = \frac{0 .7}{1 - 0.1}$

$\displaystyle \sf = \frac{0 .7}{ 0.9}$

$\displaystyle \sf = \frac{7}{ 9}$