Sum of Series 1/(1+2+...): Find Help Here

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Homework Help Overview

The discussion revolves around the sum of a series defined as 1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ..., focusing on how to find its total sum.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore rewriting the series in terms of summation notation and consider using partial fractions as a method to simplify the terms.

Discussion Status

Several participants have engaged with the problem, suggesting different approaches and expressing varying levels of understanding. Guidance has been offered regarding the use of partial fractions, and some participants have acknowledged helpful insights.

Contextual Notes

There appears to be a request for step-by-step explanations, indicating that some participants may be struggling with the underlying concepts or methods related to the series.

samii
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Given the series:

1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ...

How would u find the sum of the series?
Any help pleaseee would be very grateful! :(
 
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welcome to pf!

hi samii! welcome to pf! :smile:

(have a sigma: ∑ :wink:)
samii said:
Given the series:

1/1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) + ...

How would u find the sum of the series?
Any help pleaseee would be very grateful! :(

rewrite it as ∑ 2/n(n+1) …

does that look easier? :smile:
 
aww fanx
lol nope honestly i have NO idea how to do it :(
would u be able to explain it step by step please?
 
Last edited:
try partial fractions :wink:
 
can we write 2/n(n+1) as :

2/n - 1/(n+1)
 
almost …

2( 1/n - 1/(n+1) ) :wink:
 
Thanks that helped a lot! :D
 

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