Finding the First 4 Terms of (1-x)^-1 Expansion

In summary, the general formula for the expansion of (1-x)^-1 is 1 + x + x^2 + x^3 + ... + x^n, where n is the number of terms in the expansion. The number of terms in the expansion depends on the desired level of accuracy, and the coefficient of the x^n term is (-1)^n. However, this expansion is only valid for values of x between -1 and 1, and can be used in various fields such as physics and engineering for approximations or solving differential equations.
  • #1
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Homework Statement



To find the general series expansion (1-x)^-1 for the first 4 terms
Do i just use the taylor series ?


Homework Equations



f(x) = f(x) + f '(x)/1! x + f ''(x)/2! x^2 + f '''(x)/3! x^3

The Attempt at a Solution



= 1 + x + x^2 + x^3 + x^4 etc.

regards
Brendan
 
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  • #2
Looks good, except the taylor series of any function f around 0 is

[tex]
\sum{\frac{f^{(n)}(0)x^n}{n!}}
[/tex]
 

1. What is the general formula for the expansion of (1-x)^-1?

The general formula for the expansion of (1-x)^-1 is: 1 + x + x^2 + x^3 + ... + x^n, where n is the number of terms in the expansion.

2. How many terms should I include in the expansion?

The number of terms in the expansion depends on the desired level of accuracy. Generally, including more terms will result in a more accurate approximation of the function.

3. What is the coefficient of the x^n term in the expansion?

The coefficient of the x^n term in the expansion is equal to (-1)^n, where n is the power of x in the term. For example, the coefficient of the x^3 term is (-1)^3 = -1.

4. Can I use this expansion to approximate (1-x)^-1 for any value of x?

This expansion is only valid for values of x between -1 and 1. For values outside of this range, the expansion will not be accurate.

5. How can I use this expansion to solve problems in physics or engineering?

This expansion can be used to approximate functions in various fields, such as physics and engineering, where the inverse of (1-x) may appear. It can be particularly useful in solving differential equations or in numerical analysis.

Suggested for: Finding the First 4 Terms of (1-x)^-1 Expansion

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