For n > 1, consider the product E = (2n + 1)(2n + 3)(2n + 5)...(4n - 3)(4n - 1). Which of the following statements is true?

2^nE is divisible by the binomial coefficient 4^nC2n
2^nE is divisible by the factorial of n
The value of 2^nE divided by n! is a positive integer
The value of 2^nE divided by (4n)! is not an integer

Correct answer: The value of 2^nE divided by n! is a positive integer

Solution

The value of 2^nE divided by n! is a positive integer because the product E contains a sequence of consecutive odd numbers, ensuring divisibility by n!.

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