How do you use the binomial series to expand $(1 - x)^(-1/2)$ ?

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Answer 1 · 2015-12-16T04:12:18

$=1+ (1/2)x +(3/8)x^2 + (5/16) x^3 +..$

In the binomial expansion formula for $(1+x)^n = 1 +nx+ (n(n-1))/(2!)x^2 + ...$

substitute -x for x and $-1/2$ for n. The result would be

$1+(-1/2)(-x) + (-1/2)(-3/2) (-x)^2 /(2!) +...$

$=1+ (1/2)x +(3/8)x^2 + (5/16) x^3 +..$

How do you use the binomial series to expand (1 - x)^(-1/2)(1 - x)^(-1/2)?