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MHT CET2018MathematicsSequences and Series

The sum of the first 10 terms of the series 9 + 99 + 999 + . … . is

Options

  1. A9 8 9 10 - 1
  2. B100 9 10 9 - 1
  3. C10 9 - 1
  4. D100 9 10 10 - 1

Correct answer

B. 100 9 10 9 - 1

Step-by-step solution

S n = ( 10 − 1 + 100 − 1 + 1000 − 1 + .... ) = ( 10 + 100 + 1000 + .... ) − ( 1 + 1 + 1...... ) = 10 ( 10 n − 1 10 − 1 ) − n ⇒ S 10 = 10 ( 10 10 − 1 9 ) − 10 = 10 ( 10 10 − 1 9 − 1 ) = 10 ( 10 10 − 1 − 9 9 ) = 10 ( 10 10 − 10 9 ) = 100 9 ( 10 9 − 1 )

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