The sum of first 20 terms of the sequence 0 . 7 ,   0 . 77 ,   0 . 777 ,   . . . . . . , is :

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ......, is :
  1. 7 8 1 1 7 9 + 1 0 - 2 0
  2. 7 9 9 9 + 1 0 - 2 0
  3. 7 8 1 1 7 9 - 1 0 - 2 0
  4. 7 9 9 9 - 1 0 - 2 0

Solution

Let, S=0·7+0·77+0·777+.....,

Here, number of terms is n.

⇒S=79(0·9+0·99+0·999+....)
⇒S=79910+99102+999103+...

⇒S=7910-110+102-1102+103-1103+...

⇒S=791+1+1+1+1+...+1-110+1102+1103+...+110n
⇒S=79n-110×1-110n1-110

For the sum of 20 terms, put n=20.

⇒S=7920-110×1-110201-110

⇒S=7920-1-10-209

⇒S=781179+10-20

Asked in: JEE Main 2013 (07 Apr)

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