Question

find the sum of 10 terms of the sequence 7,7.7,7.77,7.777,..........

Answer 1

let s=7+7.7+7.77+....
= 7(1+1.1+1.11+...+1.111111111)
= (7/9)(9+9.9+9.99+....+9.999999999)
= (7/9)((10-1)+(10-0.1)+(10-0.01)+....+(10-0.000000001))
= (7/9) (10+10+10+10+10+10+10+10+10+10 -(1+0.1+0.01...0.000000001))
= (7/9)(100-1.111111111)
= 76.913580247