| \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right)...\left( 1-\frac{1}{25} \right)\] is equal to [SSC (CGL) 2010] |
A) \[\frac{2}{25}\]
B) \[\frac{1}{25}\]
C) \[1\frac{19}{25}\]
D) \[\frac{1}{325}\]
Correct Answer: A
Solution :
| \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right)...\left( 1-\frac{1}{25} \right)\] |
| \[=\left( \frac{2}{5} \right)\left( \frac{3}{4} \right)\left( \frac{4}{5} \right)...\left( \frac{24}{25} \right)=\frac{2}{25}\] |
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