Compute the sum

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589

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

Guest Jan 25, 2015

0 users composing answers..

Best Answer

+130538

+5

Let's see if we can discover a pattern....

1/3 + 1/12 + 1/30 + 1/60 + 1/105.....

1/(3*1) + 1/(6*2) + 1/(10*3) + 1/(15*4) + 1/(21*5)......

The form is

∑1/((n)(n+1)(n-1)/2) = ∑2/((n)(n+1)(n-1)) for n=2 to n=infinity

And WolframAlpha gives this sum as 1/2

CPhill Jan 25, 2015

1⁺⁰ Answers

+130538

+5

Best Answer

Let's see if we can discover a pattern....

1/3 + 1/12 + 1/30 + 1/60 + 1/105.....

1/(3*1) + 1/(6*2) + 1/(10*3) + 1/(15*4) + 1/(21*5)......

The form is

∑1/((n)(n+1)(n-1)/2) = ∑2/((n)(n+1)(n-1)) for n=2 to n=infinity

And WolframAlpha gives this sum as 1/2

CPhill Jan 25, 2015

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