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Question 210029
JEE Mathematics · Hard

Sequences and Series: Vn method MCQ

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Vn methodHardQuestion 210029

Question

The sum 1/(1×3) + 1/(3×5) + 1/(5×7) + ... to n terms is:
  1. A
    n/(2n+1)
    Correct
  2. B
    n/(4n+2)
  3. C
    1/(2n+1)
  4. D
    n/2(2n+1)

Correct answer

n/(2n+1)

Explanation

General term = 1/((2r−1)(2r+1)) = (1/2)[1/(2r−1) − 1/(2r+1)]. Telescoping n terms: (1/2)[1 − 1/(2n+1)] = (1/2)[2n/(2n+1)] = n/(2n+1).

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