Find the sum of each of the following infinite series :

Question:

Find the sum of each of the following infinite series :

$6+1.2+0.24+\ldots \ldots \infty$

 

Solution:

It is Infinite Geometric Series.

Here, a=6

$r=\frac{1.2}{6}=\frac{2}{10}=0.2$

The formula used: Sum of an infinite Geometric series $=\frac{\mathrm{a}}{1-\mathrm{r}}$

$\therefore$ Sum $=\frac{6}{1-0.2}=\frac{6}{0.8}=\frac{15}{2}$

Sum $=\frac{15}{2}$

 

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