For any real number p we may express (1 + x)P as a power series (1...

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For any real number p we may express (1 + x)P as a power series (1 + x) = 1 + px + p(p-1)+ 2! k=D0 IIp-j) The series, called the binomial series converges for -1 <x < 1 for any real k! where number p. (a) (4 points) Is this series expansion and definition of (2) for non-integer p consistent with previous definitions and theorems? Explain. (b) (6 points) Use the binomial series to write an expansion and find a closed form for Cn. For any real number p we may express (1 + x)P as a power series (1 + x) = 1 + px + p(p-1)+ 2! k=D0 IIp-j) The series, called the binomial series converges for -1 <x < 1 for any real k! where number p. (a) (4 points) Is this series expansion and definition of (2) for non-integer p consistent with previous definitions and theorems? Explain. (b) (6 points) Use the binomial series to write an expansion and find a closed form for Cn.