+0

# Difficult math question

0
273
2
+11

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

#1
+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
+6185
+3

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

Rom Jan 18, 2019
#2
+24859
+7

Compute the sum

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

Jan 18, 2019
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