Question

when simplified the product (1-1/3)(1-1/4)(1-1/5)....... (1-1/n) a)1/n b)2/n c)2(n-1)/n d)2/n(n-1)​

Answer 1

Answer:

(b) $\frac{2}{n}$

Step-by-step explanation:

$(1 - \frac{1}{3} ) \times (1 - \frac{1}{4} ) \times (1 - \frac{1}{5} ) \times ............... \times (1 - \frac{1}{n} )$

= $(\frac{3-1}{3} ) \times (\frac{4-1}{4} ) \times (\frac{5-1}{5} ) \times ............... \times ( \frac{n-1}{n} )$

= $(\frac{2}{3} ) \times (\frac{3}{4} ) \times (\frac{4}{5} ) \times ............... \times ( \frac{n-1}{n} )$

= $(\frac{2}{n} )$