# How do you find the Maclaurin series for #ln((1+x)/(1-x))#?

The Maclaurin Series is what we're looking for.

We may begin with a widely recognized standard series.

Because of the logs' property, we can rewrite the original function as follows:

Substituting the two series mentioned above, we obtain:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the Maclaurin series for ln((1+x)/(1-x)), you can start by expanding ln(1+x) and ln(1-x) using their respective Maclaurin series.

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

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

Now, subtract the series for ln(1-x) from ln(1+x):

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

= x + (x^2/2 + x^2/2) + (x^3/3 + x^3/3) + (x^4/4 + x^4/4) + ...

Simplify the expression:

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

This is the Maclaurin series for ln((1+x)/(1-x)).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you find the taylor series of #1 1x^2#?
- How do you do the taylor series expansion of #arctan(x)# and #xsinx#?
- How do you find the maclaurin series expansion of #f(x)=(1-x)^-2#?
- What is the interval of convergence of #sum_{k=0}^oo 2^(k) / ((2k)!* x^(k)) #?
- Find the sum of the series: #sum_{n=5}^ ∞ 6 / (n^2 - 3n)# ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7