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Compute the sum
 

\(\frac{2}{1 \cdot 2 \cdot 3} + \frac{2}{2 \cdot 3 \cdot 4} + \frac{2}{3 \cdot 4 \cdot 5} + \cdots\)

 Jan 18, 2019

Best Answer 

 #1
avatar+6185 
+3

\(\sum \limits_{n=0}^\infty \dfrac{n!}{(n+1+\delta)!} = \dfrac{1}{\delta \cdot \delta!}\\ 2\sum \limits_{n=0}^\infty \dfrac{n!}{(n+3)!} = \dfrac{2}{2\cdot 2!} = \dfrac 1 2\)

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 Jan 18, 2019
 #1
avatar+6185 
+3
Best Answer

\(\sum \limits_{n=0}^\infty \dfrac{n!}{(n+1+\delta)!} = \dfrac{1}{\delta \cdot \delta!}\\ 2\sum \limits_{n=0}^\infty \dfrac{n!}{(n+3)!} = \dfrac{2}{2\cdot 2!} = \dfrac 1 2\)

Rom Jan 18, 2019
 #2
avatar+24859 
+7

Compute the sum

\(\frac{2}{1 \cdot 2 \cdot 3} + \frac{2}{2 \cdot 3 \cdot 4} + \frac{2}{3 \cdot 4 \cdot 5} + \cdots\)

 

answer see: https://web2.0calc.com/questions/algebra_47009#r4

 

laugh

 Jan 18, 2019

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