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# Sequences/Series

0
31
2

Calculate:

$$\left(1 - \frac12 \right) \cdot \left(1 - \frac13 \right) \cdot \left(1 - \frac14\right) \dotsm \left(1 - \frac {1}{2009} \right)$$

Sep 21, 2022

### 2+0 Answers

#1
0

I feel like there's a way that we can factor out $$1$$from it then multiply the fractions but I have absolutely no idea where to go from there.

Sep 21, 2022
#2
+117834
+1

$$\left(1 - \frac12 \right) \cdot \left(1 - \frac13 \right) \cdot \left(1 - \frac14\right) \dotsm \left(1 - \frac {1}{2009} \right) \\=\left(\frac{1}{2}\right) \cdot \left(\frac{2}{3} \right) \cdot \left(\frac{3}{4}\right) \dotsm \left(\frac{2008}{2009} \right) \\=\frac{1}{2009}$$

The rest cancels out.

Sep 21, 2022