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Compute the sum $$\frac{2}{1 \cdot 2 \cdot 3} + \frac{2}{2 \cdot 3 \cdot 4} + \frac{2}{3 \cdot 4 \cdot 5} + \cdots$$

 Sep 10, 2017
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Sum(n=1)^m [2/(n (n + 1))] = 2m/(m+1) = 2 - 2/(m + 1).
If m = 1,000,000, then we have:
[2 x 1,000,000] / [1,000,000 +1] =1.9999980000019999980.....etc.
=~2 it converges to 2.

 Sep 10, 2017

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