Question

The simplest value of $(1-\frac{1}{y})(1-\frac{1}{y+1})(1-\frac{1}{y+2})\cdot \cdot \cdot \cdot (1-\frac{1}{y+y})$ is

• A. $\frac{1}{y}$
• B. $\frac{1}{2y}$
• C. $\frac{y-1}{2y}$
• D. $\frac{2y}{y-1}$

Answer 1

The correct option is C $\frac{y-1}{2y}$

$(1-\frac{1}{y})(1-\frac{1}{y+1})(1-\frac{1}{y+2})............(1-\frac{1}{y+y})$

$\left(\frac{y-1}{y}\right)\left(\frac{y+1-1}{y+1}\right)\left(\frac{y+2-1}{y+2}\right).............\left(\frac{y+y-1}{y+y}\right)$

=$\frac{y-1}{2y}$