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The sum of the series 1 1+ 2 + 1 2 + 3 + 1 3 + 4 + upto 15 terms is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Given series is aligned & 1 1+ 2 + 1 2 + 3 + 1 3 + 4 + . . & n^ th term = 1 n + n+1 & 15^ th term = 1 15 + 16 aligned Thus, given series upto 15 terms is 1 1+ 2 + 1 2 + 3 + 1 3 + 4 + + 1 15 + 16 This can be re-written as 1- 2 -1 + 2 - 3 -1 + 3 - 4 -1 + + 15 - 16 -1 (By rationalization) gathered =-1+ 2 - 2 + 3 - 3 + 4 + . .- 14 + 15 - 15 + 16 =-1+ 16 =-1+4=3 gathered Hence, the required sum =3

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