When simplified the product : $$\left( {2 - \frac{1}{3}} \right)$$ $$\left( {2 - \frac{3}{5}} \right)$$ $$\left( {2 - \frac{5}{7}} \right)$$ .....$$\left( {2 - \frac{{997}}{{999}}} \right)$$
A. $$\frac{1001}{3}$$
B. $$\frac{5}{3}$$
C. $$\frac{5}{999}$$
D. $$\frac{1001}{999}$$
Answer: Option A
Solution(By Examveda Team)
According to the question,$$ \Rightarrow \left( {2 - \frac{1}{3}} \right)\left( {2 - \frac{3}{5}} \right)\left( {2 - \frac{5}{7}} \right).....$$ $$\left( {2 - \frac{{997}}{{999}}} \right)$$
$$\eqalign{ & \Rightarrow \frac{5}{3} \times \frac{7}{5} \times \frac{9}{7}.....\frac{{1001}}{{999}} \cr & \Rightarrow \frac{1}{3} \times 1001 \cr & \Rightarrow \frac{{1001}}{3} \cr} $$
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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