Calculate Sums with F(i) Function for Math Problem

  • Thread starter daniel_i_l
  • Start date
  • Tags
    Sums
In summary, the conversation discusses how to calculate the sum of a given function using the fact that the sum of a function minus the sum of the previous term is equal to the function of the current term minus the function of the first term. The person mentions choosing a specific function and value for r, but runs into an issue with an undefined term. Another person suggests a simpler approach using partial fractions.
  • #1
daniel_i_l
Gold Member
868
0
I need to calculate
[tex]
\sum_{i=1}^n \frac{1}{i(i+1)}
[/tex]
useing the fact that:
[tex]
\sum_{i=1}^n F(i) - F(i-1) = F(n) - F(0)
[/tex]
now I chose the function
[tex]
F(i) = \frac{1}{i} \frac{1}{(i+1)} ... \frac{1}{(i+r)}
[/tex]
so
[tex]
F(i)-F(i-1)=(\frac{1}{i}\frac{1}{(i+1)} ... \frac{1}{(i+r-1)})(\frac{1}{(i+r)}-\frac{1}{(i-1)})
[/tex]
now I want to use that to calcualte the sum chooseing r as 2, but I'm stuck because the F(0) is undefined, and because of the
[tex]
\frac{1}{i+r}-\frac{1}{i-1})
[/tex]
 
Last edited:
Physics news on Phys.org
  • #2
You need to choose F(i) so that

[tex]
F(i)-F(i-1)=\frac{1}{i(i+1)}
[/tex]

Your choice of F(i) does not satisfy this (what is that r anyways?) Try another choice of F, with a hint-think partial fractions.
 
  • #3
Why on Earth would you choose that three term nightmare for F? There is a much easier way to do it. Hint: what is [tex] \frac{1}{i+1} - \frac{1}{i} [/tex]?
 
  • #4
Thanks a lot!
 

What is the purpose of the F(i) function in math problems?

The F(i) function is used to denote a specific sequence or pattern in a mathematical problem. It allows for a simplified representation of a complex series of numbers or operations.

How do you calculate sums using the F(i) function?

To calculate sums using the F(i) function, you must first determine the starting value of i, the ending value of i, and the pattern or formula represented by F(i). Then, plug these values into the appropriate formula to find the sum.

Can the F(i) function be used for any type of mathematical problem?

Yes, the F(i) function can be used for a wide range of mathematical problems, including sequences, series, and functions.

What is the difference between using the F(i) function and a regular summation notation?

The F(i) function is typically used for simpler, more straightforward problems, while regular summation notation is used for more complex and abstract problems. Additionally, the F(i) function may be used for specific sequences or patterns, while summation notation can be used for a wider range of problems.

Are there any limitations to using the F(i) function for calculations?

While the F(i) function can be a useful tool for solving mathematical problems, it may not always be the most efficient or accurate method. It is important to consider the limitations of the F(i) function and choose the best method for each individual problem.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
355
  • Calculus and Beyond Homework Help
Replies
6
Views
274
  • Calculus and Beyond Homework Help
Replies
4
Views
604
  • Calculus and Beyond Homework Help
Replies
1
Views
253
  • Calculus and Beyond Homework Help
Replies
15
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
635
  • Calculus and Beyond Homework Help
Replies
9
Views
875
  • Calculus and Beyond Homework Help
Replies
16
Views
475
  • Calculus and Beyond Homework Help
Replies
1
Views
556
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
Back
Top