Sum of the first 50 terms of 1/(n(n+1))

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In summary, the conversation is about solving for the sum of the first 50 terms of 1/(n(n+1)). The person asking the question is not sure how to find the sum and is seeking help. Another person suggests using partial fractions to easily solve the sum. The person asking the question initially does not understand how partial fractions would help, but then figures it out and thanks the other person for their help.
  • #1
nate808
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how would you solve for the sum of the first 50 terms of 1/(n(n+1))
I know how to do it if there is a common denominator--but i can't seem to find one here, can someone please help(btw, question on a test i just had that i couldt figure out, not hw)
 
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  • #2
Are you familiar with partial fractions? If so then you can do the sum very easily! :)
 
  • #3
Any question related to your coursework should go in homework help, even questions about old exams. :smile: Hang on, I'm going to send the thread for a ride over!
 
  • #4
i don't exactly understand what finding a partial fraction would do in order to help find the sum--could u please explain( i believe the partial fractions ar 1/n - 1/n+1
 
  • #5
nvm--i figured it out--thanks for the help
 

Related to Sum of the first 50 terms of 1/(n(n+1))

What is the formula for the sum of the first 50 terms of 1/(n(n+1))?

The formula for the sum of the first 50 terms of 1/(n(n+1)) is (50/51) - (1/51)(1/52).

How do you derive the formula for the sum of the first 50 terms of 1/(n(n+1))?

The formula can be derived using the partial fraction decomposition method and then using the formula for the sum of an arithmetic series.

Can the formula for the sum of the first 50 terms of 1/(n(n+1)) be generalized for any given number of terms?

Yes, the formula can be generalized for any given number of terms by replacing 50 with the desired number of terms in the formula.

Is there a simpler way to calculate the sum of the first 50 terms of 1/(n(n+1)) without using the formula?

Yes, the sum can be calculated using a recursive function or by using a calculator or spreadsheet.

What is the significance of studying the sum of the first 50 terms of 1/(n(n+1))?

The study of this sum can help understand concepts such as series, partial fractions, and arithmetic sequences. It also has applications in fields such as mathematics, physics, and computer science.

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