Question

Sum of series
1+0.6+0.06+0.006+.........

Answer 1

1,666...
(16-1) / 90
15/90= 1/6

Answer 2

so, the sequence is hmm, well
it is the sum of the sequence where 0.6 is the initial term and each term is 1/10 of the previous
then add 1 to that
so rmember the 1 at the end
the sum is 1.66666666666666 forever actually
but to calculate the inifntie sequence (without the 1)
sum of inifnite is (a1)/(1-r) where a1=first term and r=common ratio

a1=0.6
r=1/10=0.1
so
the sum is 0.6/(1-0.1)=0.6/0.9=6/9
add 1
1=9/9 so
1+6/9=9/9+6/9=15/9

the sum is equal to 15/9 or 1 and 6/9 or 1.66666666666666666666666666666666666666