Q82 / 150 · MHT CET 2018 · Mathematics

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

  • A
    98910-1
  • Correct answer
    B
    1009109-1
  • C
    109-1
  • D
    10091010-1

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 )

Hence, the correct answer is option: 'B'.

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