Binomial Theorem Negative & Fractional Exponents

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At the beginning of the video, dosen't the summation go from k = 0 to k = \alpha. I don't see how it's an infinite series.

NeelSandellISAWESOME
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Could you apply Maclaurin series here rather than memorising the formula for binomial expansion with fractional and negative indices?

mrigayu