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 $$frac{0.6}{1-0.1}$$ = $$frac{2}{3}$$

Now the total sum will be 1+$$frac{2}{3}$$ = 1$$frac{2}{3}$$