Exams › JEE Main › Maths

Let C0, C1, C2,..., Cn denote the coefficients in the expansion of (1 + x)ⁿ. Then the value of 2²·C0/(1·2) + 2³·C1/(2·3) +... + 2^(n+2)·Cn/((n+1)(n+2)) is

1. (3^(n+1) - 2n - 5)/((n+1)(n+2))
2. (3^(n+2) - 2n - 5)/((n+1)(n+2))
3. (3^(n+2) + 2n - 5)/((n+1)(n+2))
4. None of these

Correct answer: (3^(n+2) - 2n - 5)/((n+1)(n+2))

Solution

The sum equals (3^(n+2) - 2n - 5)/((n+1)(n+2)); this matches direct evaluation for n = 1,2,3,4 (e.g. n=1 gives 10/3, n=2 gives 6).

Related JEE Main Maths questions

• Let Pn = cosⁿ θ + sinⁿ θ. If Pn - Pn-2 = k Pn-4, then the value of k is:
• For any natural number n, the expression x^(2n - 1) + y^(2n - 1) is divisible by which of the following?
• For a natural number n, which of the following always divides the expression x^(n+1) + (x + 1)^(2n−1)?
• For a positive integer n, the expression 5^(2n+2) − 24n − 25 is divisible by which of the following?
• For every natural number n, the expression 41ⁿ − 14ⁿ is divisible by which of the following?
• Let C0, C1, C2,..., C15 denote the binomial coefficients in the expansion of (1 + x)¹⁵. Then the value of C1/C0 + C2/C1 + C3/C2 +... + C15/C14 is:

⚔️ Practice JEE Main Maths free + battle 1v1 →