The sum of the series (1 + 0.6 + 0.06 + 0.006 + 0.0006 + ....) is
Given:
Summation of numbers (1 + 0.6 + 0.06....)
as we can see that the sequence 0.6, 0.06, 0.006 is making infinite g.p. with common ratio of 0.1
as we know summation of an infinite g.p. is $$\frac{a}{1-r}$$ (where a is first term and r is common ratio)
hence summation will be $$\frac{0.6}{1-0.1}$$ =Â $$\frac{2}{3}$$
Now the total sum will be 1+$$\frac{2}{3}$$ = 1$$\frac{2}{3}$$
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