\( \Large \left(1-\frac{1}{2}\right) \left(1-\frac{1}{3}\right) \left(1-\frac{1}{4}\right) \left(1-\frac{1}{5}\right)...... \left(1-\frac{1}{m}\right)=? \)

A) \( \Large \frac{1}{m} \)

B) m

C) m+1

D) \( \Large \frac{1}{ \left(m-1\right) } \)

Correct answer:
A) \( \Large \frac{1}{m} \)

Description for Correct answer:
Given expression

=\( \Large \left(1-\frac{1}{2}\right) \left(1-\frac{1}{3}\right) \left(1-\frac{1}{4}\right) \left(1-\frac{1}{5} \right)...\left(1-\frac{1}{m-1}\right) \left(1-\frac{1}{m}\right) \)

=\( \Large \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times ... \times \frac{m-2}{m-1} \times \frac{m-1}{m}=\frac{1}{m} \)


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