The equation of motion of a particle executing simple harmonic motion is a +16π²x=0 in this equation ais linear acceleration if particle at a displacement x the time period in simple harmonic motion is

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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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