# How do you find the taylor series of #1 1x^2#?

The Taylor series basically hands us back

So

and the Taylor series is:

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

To find the Taylor series of ( \frac{1}{1-x^2} ), we first note that this function can be expressed as a geometric series:

[ \frac{1}{1 - x^2} = 1 + x^2 + (x^2)^2 + (x^2)^3 + \ldots ]

Now, we can use the formula for the sum of an infinite geometric series:

[ S = \frac{a}{1 - r} ]

Where ( a ) is the first term and ( r ) is the common ratio. In this case, ( a = 1 ) and ( r = x^2 ).

So, the Taylor series expansion of ( \frac{1}{1-x^2} ) is:

[ 1 + x^2 + x^4 + x^6 + \ldots ]

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

- How do you find the Maclaurin Series for #f(x) = ln(cosx)#?
- How i calculate the value of the sum #2^(n+3)/(n!)# ?
- How to calculate this sum? #S=(x+1/x)^2+(x^2+1/(x^2))^2+...+(x^n+1/(x^n))^2#.
- How do you find the power series for #f(x)=e^(-4x)# and determine its radius of convergence?
- How do you calculate Euler's Number?

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