Q:

What is the Maclaurin series for ln(1+x)?

A:

The Maclaurin series for ln(1+x) is ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x. This series gives an approximate value of ln(1+x) when x is between minus one and one. The more terms are included, the more accurate the value will be.

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A Maclaurin series is an expansion of the Taylor series around zero. A Taylor series is a power series expansion that gives an approximate value of a function. The general formula for a Maclaurin series is f(x) = f(0) + f'(0)x + f''(0)x^2/2! + x, where f'(0) is the derivative of f(x) with respect to x at x = 0, f''(0) is the second derivative and so on.

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