Hey Divya

Solution (S):

S = 0.7+0.77+0.777+....0.7777

=7(0.1+0.11+0.11+0.111+.......+0.1111....)

= 79[0.9+0.99+0.99+0.999+...........)

=79[(1−0.1)+(1−0.01)+....+(1−0.000......1)]

=7/9 * [20 − (1 / 10+1 / 10^2+......1 / 20^20)]

Therefore, a= r = 1/10

=7/ 9* [20−1/9 * (1−10^−20)

=7 / 81 * [179 + 10^−20]  -> Answer