Question 130

The value of the following is:
$$(2-\frac{1}{3})(2-\frac{3}{5})(2-\frac{5}{7}).........(2-\frac{997}{999})$$

Solution

Expression : $$(2-\frac{1}{3})(2-\frac{3}{5})(2-\frac{5}{7}).........(2-\frac{997}{999})$$

= $$(\frac{5}{3})(\frac{7}{5})(\frac{9}{7})............(\frac{999}{997})(\frac{1001}{999})$$

(Now, numerator of each term will get cancelled by the denominator of the next term, and we are left with)

= $$\frac{1001}{3}$$

=> Ans - (A)

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The value of the following is:$$(2-\frac{1}{3})(2-\frac{3}{5})(2-\frac{5}{7}).........(2-\frac{997}{999})$$