The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,...., is
781(179+10−20)
Given sequence can be written as
710+77100+777103+...+ up to 20 terms
=7[110+11100+111103+...+upto20terms]
Multiply and divide by 9
79[(1−110+(1−1102)+(1−1103))+.....up to 20 terms]=79[20−110(1−(110)20)1−110]=79[1799+19(110)20]=781[179+(10)−20]