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