JEE Probability

If A1,A2,A3.....A1006A_{1},A_{2},A_{3}.....A_{1006} be independent events such that P(Ai)=12i(i=1,2,3....1006)P(A_{i})=\frac{1}{2i}(i=1,2,3....1006) and probability that none of the events occurs be α!2α(β!)2\frac{\alpha!}{2^{\alpha}(\beta!)^{2}}, then

A)A)- β\beta is of form 4k+24k+2 where kk is a positive integer.

B)B)- α=2β\alpha=2\beta

C)C)- β\beta is a composite number

D)D)- α\alpha is of form 4k4k where where kk is a positive integer.

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