# How do you find the power series of ln(1+x)?

with radius of convergence

Start from:

so:

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To find the power series of ln(1+x), we can start with the known Maclaurin series expansion of ln(1+x), which is:

ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ...

This series converges for |x| < 1. Therefore, the power series expansion for ln(1+x) is simply the Maclaurin series expansion given above.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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