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Nice sum (Posted on 2004-08-24) Difficulty: 3 of 5
Give a closed expression for the infinite sum:

1/1 + 2/(2+3) + 3/(4+5+6) + 4/(7+8+9+10) + ...

See The Solution Submitted by Federico Kereki    
Rating: 2.7500 (4 votes)

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Solution | Comment 9 of 13 |

It seems to me that the solution is

(x/(((x^2+x)/2)^2+(x^2+x)-(((x-1)^2+x-1)/2)^2+((x-1)^2+x-1)/2)

from 1 to .

Assuming the same range, this simplifies to

(x/((x^3+x)/2))

or 2*(2/(x^2+x)

or 2*1, which is 2.


  Posted by Keith Steele on 2004-08-30 20:10:09
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