Find an expression in terms of n for summation

In summary, the conversation discusses solving a problem involving partial fractions and finding an expression for the summation of a series. The first part of the problem has already been solved, but the individual is seeking help with the second part and asks for clues to show that the summation is always less than 7/4.
  • #1
elitewarr
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0

Homework Statement


By first expressing the general term in partial fractions, find an expression in terms of n for
summation of r=2 to n ( 1 / (r^2 - 1) ). Hence show that summation of r=1 to n ( 1 / r^2) i less than 7/4 for all values of n


Homework Equations





The Attempt at a Solution


I solved the first part of the question already. However, I'm stuck at the second part. Can anyone give me some clues to showing 1/r^2 sum from r = 1 to n is always less than 7/4?
Thank you.
 
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  • #2


Well, what did you get for the first part? I suspect that is important to solving the second part!
 

Related to Find an expression in terms of n for summation

1. What is the meaning of "find an expression in terms of n for summation"?

"Find an expression in terms of n for summation" refers to the process of writing a mathematical expression that represents the sum of a given set of numbers, where the number of terms in the sum is represented by the variable n.

2. How do you find an expression in terms of n for summation?

To find an expression in terms of n for summation, you first need to identify the pattern or rule that the numbers in the given set follow. Then, you can use this pattern to write a general expression that represents the sum of n terms. This expression will include the variable n, which represents the number of terms in the sum.

3. Can you provide an example of finding an expression in terms of n for summation?

Sure, for example, if we have the set of numbers {2, 5, 8, 11, 14}, we can see that each number is 3 more than the previous one. So, the general expression for finding the sum of n terms in this set would be 2 + (2 + 3) + (2 + 6) + (2 + 9) + ... + (2 + 3(n-1)), where n represents the number of terms in the sum.

4. What is the purpose of finding an expression in terms of n for summation?

The purpose of finding an expression in terms of n for summation is to have a general formula that can be used to find the sum of any number of terms in the given set. This can be useful in various mathematical calculations and also helps in understanding the pattern or rule followed by the numbers in the set.

5. Are there any other ways to write an expression for summation?

Yes, there are other ways to write an expression for summation, such as using the sigma notation (Σ) or using the recursive formula. However, finding an expression in terms of n for summation is a common and straightforward method that can be applied to most sets of numbers.

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