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

[samii]

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! :(

 

[tiny-tim]

welcome to pf!

hi samii! welcome to pf!

(have a sigma: ∑ )

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? ​

 

[samii]

aww fanx
lol nope honestly i have NO idea how to do it :(
would u be able to explain it step by step please?

 

[tiny-tim]

try partial fractions

 

[samii]

can we write 2/n(n+1) as :

2/n - 1/(n+1)

 

[tiny-tim]

almost …

2( 1/n - 1/(n+1) )

 

[samii]

Thanks that helped alot! :D