Question

0.1 + 0.11 + 0.111 + . . . . + 0.1111111111 .

How to do this question, please give an explanation

Answer 1

Check out this attachment

Answer 2

Step-by-step explanation:

Sn= 0.1+0.11+0.111.....0.1111111111

dividing and multiplying with 9

we get

Sn=1/9[0.9+0.99+0.999+.....0.9999999999]

=1/9[1-0.1 + 1-0.01 + 1-0.001 +......+1-0.0000000001]

=1/9[ n - ( 0.1+0.01+0.001+....+0.0000000001)

=1/9[ n - 0.1( 1 - 10^n)/-9]

=1/9[ n + 0.1( 1 - 10^n)/9]