Question

The simplified value of
$(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})$...$(1-\frac{1}{99})(1-\frac{1}{100})$

• A. $\frac{2}{99}$
• B. $\frac{1}{25}$
• C. $\frac{1}{50}$
• D. $\frac{1}{100}$

Answer 1

The correct option is C $\frac{1}{50}$

Given expression

$=\frac{2}{3_1}\times \frac{3^1}{4_1}\times \frac{4^1}{5}\times ....\times \frac{98}{{99}_1}\times \frac{{99}^1}{100}$

$=\frac{2}{100}=\frac{1}{50}$ (All others cancel out)