the distance of closest approach of a proton h+fired towards cu is x and what would be the distance of closest approach of an alpha particle if it is fired towards with half of the kinetic energy of proton towards cu

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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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