Help Factorial Partial Fraction Decomposition

In summary, "Help Factorial Partial Fraction Decomposition" is a method used in calculus to simplify rational functions for easier integration. It is important in various applications and works by breaking down the function into simpler fractions. It can be used for any rational function, but may have limitations for higher degree functions and non-rational functions.
  • #1
danerape
32
0

Homework Statement



Show that n/(n+1)!=(1/n)-(1/(n+1)!)

I am totally lost on the algebraic steps taken to come to this conclusion. It is for an
Infinite series.

Thanks
 
Physics news on Phys.org
  • #2
It's not true. For example, take n=3. Then
[tex]\frac{n}{(n+1)!} = \frac{3}{4!} = \frac{3}{24} = \frac{1}{8}[/tex]but
[tex]\frac{1}{n}-\frac{1}{(n+1)!} = \frac{1}{3}-\frac{1}{24} = \frac{8}{24}-\frac{1}{24} = \frac{7}{24}[/tex]
 
  • #3
n/(n+1)!= 1/n! - 1/(n+1)!
 
  • #4
Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!
 
  • #5
It's easy to prove. In the LHS write n=(n+1)-1.
 
  • #6
Wow, that is pretty obvious, I haven't had any experience with ! before this though. Thanks alot!

Dane
 

1. What is "Help Factorial Partial Fraction Decomposition"?

"Help Factorial Partial Fraction Decomposition" is a method used in mathematics, specifically in calculus, to decompose a rational function into simpler fractions. It is particularly useful in solving integrals involving rational functions.

2. Why is "Help Factorial Partial Fraction Decomposition" important?

"Help Factorial Partial Fraction Decomposition" is important because it allows us to simplify complex rational functions, making them easier to integrate. It is also a fundamental concept in calculus and is used in various applications, such as in engineering and physics.

3. How does "Help Factorial Partial Fraction Decomposition" work?

The method involves breaking down a rational function into partial fractions with numerator terms of a lower degree than the denominator. The coefficients of these partial fractions are then determined using algebraic techniques, such as equating coefficients or using the method of undetermined coefficients.

4. Can "Help Factorial Partial Fraction Decomposition" be used for any rational function?

Yes, "Help Factorial Partial Fraction Decomposition" can be used for any rational function, as long as the degree of the numerator is less than the degree of the denominator. However, if the function has repeated or complex roots, additional steps may be required.

5. Are there any limitations to "Help Factorial Partial Fraction Decomposition"?

One limitation of "Help Factorial Partial Fraction Decomposition" is that it only works for rational functions. It cannot be used for irrational functions or functions with transcendental terms. Additionally, the method may not always yield a simple and concise result, especially for higher degree functions.

Similar threads

  • Calculus and Beyond Homework Help
Replies
8
Views
929
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
12
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
891
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top