# How do you use the binomial series to expand #sqrt(z^2-1)#?

Thus, the extension will be as follows:

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To expand sqrt(z^2 - 1) using the binomial series, we first need to express sqrt(z^2 - 1) as a binomial function. One common approach is to rewrite the expression as (1 - (1 - z^2))^0.5. Then, we apply the binomial series expansion formula, which states that (1 + x)^n = Σ(nCr * x^r), where Σ denotes the sum from r = 0 to ∞, and nCr represents the binomial coefficient "n choose r". Substituting x = -u and n = 0.5 into the formula, we obtain the expansion of sqrt(z^2 - 1).

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