Question : When simplified, the product $(2- \frac{1}{3}) (2-\frac{3}{5}) (2- \frac{5}{7}) .... (2- \frac{997}{999})$ equals:
Option 1: $\frac{5}{999}$
Option 2: $\frac{5}{3}$
Option 3: $\frac{1001}{999}$
Option 4: $\frac{1001}{3}$
Answer (1)
25th Jan, 2024
Correct Answer: $\frac{1001}{3}$
Solution :
Given: $(2- \frac{1}{3}) (2-\frac{3}{5}) (2- \frac{5}{7}) .... (2- \frac{997}{999})$
= $\frac{5}{3}×\frac{7}{5}×\frac{9}{7} .... ×\frac{1001}{999}$
= $\frac{1001}{3}$
Hence, the correct answer is $\frac{1001}{3}$.
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