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I don't know how to solve this, can someone help as soon as possible? Thank you!

 

Compute the sum:

 

\(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}...\)

Guest Jun 4, 2017
 #1
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The denominators follow this pattern: n^3 + 3n^2 + 2n. Therefore they all sum up to:

∑[ 2 / ( n^3 + 3 n^2 + 2 n), n, 1, 1,000,000] = 1/2.

Guest Jun 4, 2017
 #2
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Thank you so much!

Guest Jun 5, 2017

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