The number of positive integers n such that 2n di vides n! is

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exactly 1

exactly 2

infinite

none of these

answer is D.

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Detailed Solution

The exponent of 2 in n! is given byE=n2+n22+n23+…where [x] denotes greatest integer ≤x, As [x]≤x ∀xn2m=0 after finite number of terms. Thus we getE

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