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

Options

  1. A7 8 1 1 7 9 + 1 0 - 2 0
  2. B7 9 9 9 + 1 0 - 2 0
  3. C7 8 1 1 7 9 - 1 0 - 2 0
  4. D7 9 9 9 - 1 0 - 2 0

Correct answer

A. 7 8 1 1 7 9 + 1 0 - 2 0

Step-by-step solution

Let, S = 0 · 7 + 0 · 7 7 + 0 · 7 7 7 + . .... , Here, number of terms is n . ⇒ S = 7 9 ( 0 · 9 + 0 · 99 + 0 · 999 + . ...) ⇒ S = 7 9 9 10 + 99 10 2 + 999 10 3 + . . . ⇒ S = 7 9 10 - 1 10 + 10 2 - 1 10 2 + 10 3 - 1 10 3 + . . . ⇒ S = 7 9 1 + 1 + 1 + 1 + 1 + . . . + 1 - 1 10 + 1 10 2 + 1 10 3 + . . . + 1 10 n ⇒ S = 7 9 n - 1 10 × 1 - 1 10 n 1 - 1 10 For the sum of 20 terms, put n = 20 . ⇒ S = 7 9 2 0 - 1 1 0 × 1 - 1 1 0 2 0 1 - 1 1 0 ⇒S

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