if from (1,a) two tangents can be drawn on exactly one branch of the hyperbola x^2/4-y^2/1=1,then what is the range of a?

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Sum of series 2[n/2] ! [n/2]!/ n! [2Co-2C2+3C2....+[-1]^n[n+1]2Cn] where n is an even positive integer. Kindly provide solution of this question and how to generalise this. How do we know that which expansion will give this?

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