| \[\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right)...\left( 1-\frac{1}{m} \right)=?\] |
A) \[\frac{1}{m}\]
B) \[m\]
C) \[m+1\]
D) \[\frac{1}{(m-1)}\]
E) None of these
Correct Answer: A
Solution :
| Given expression |
| \[=\left( 1-\frac{1}{2} \right)\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right)...\left( 1-\frac{1}{m-1} \right)\left( 1-\frac{1}{m} \right)\]\[=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times ...\times \frac{(m-2)}{(m-1)}\times \frac{(m-1)}{m}=\frac{1}{m}\] |
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