Let, S=0⋅7+0⋅77+0⋅777+.....,
Here, number of terms is n.
⇒S=97(0⋅9+0⋅99+0⋅999+....)
⇒S=97(109+10299+103999+...)
⇒S=97(1010−1+102102−1+103103−1+...)
⇒S=97(1+1+1+1+1+...+1)−(101+1021+1031+...+10n1)
⇒S=97(n−101×1−101(1−10n1))
For the sum of 20 terms, put n=20.
⇒S=97(20−101×1−101(1−10201))
⇒S=97(20−91−10−20)
⇒S=817(179+10−20)