Exams › JEE Main › Maths

Using mathematical induction, the sum 1/(1·2·3) + 1/(2·3·4) +... + 1/((n+1)(n+2)) is equal to

1. n(n+1)/(4(n+2)(n+3))
2. n(n+3)/(4(n+1)(n+2))
3. n(n+2)/(4(n+1)(n+3))
4. None of these

Correct answer: n(n+3)/(4(n+1)(n+2))

Solution

The correct option is derived from the formula for the sum of the series, which can be proven using mathematical induction. By establishing a base case and showing that if the formula holds for n, it also holds for n+1, we confirm that the sum simplifies to n(n+3)/(4(n+1)(n+2)).

Related JEE Main Maths questions

• If Sₙ = cosⁿ θ + sinⁿ θ, then the value of 3S₄ - 2S₆ is
• For a natural number n, the inequality 2^(n - 1) < nⁿ holds when
• For any natural number n, the product n(n + 1) is always
• For which positive integers n does the inequality 3ⁿ exceed n³?
• For which values of n does the inequality 4ⁿ/(n+1) < (2n)!/(n!)² hold, if P(n) denotes this statement?
• For a positive integer n, define a(n) = 1 + 1/2 + 1/3 + 1/4 +... + 1/(2ⁿ - 1). Which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →