Which of the following statement(s) is/are TRUE?
I. $$\left(1 + \frac{1}{2}\right)\left(1 + \frac{1}{3}\right)\left(1 + \frac{1}{4}\right).......\left(1 + \frac{1}{998}\right)>497$$
II. $$14\frac{3}{4} + 5\frac{1}{4} - 2\frac{1}{2}>11\frac{1}{8}+12\frac{3}{8}-7\frac{1}{4}$$
$$\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right).......\left(1+\frac{1}{998}\right)>497$$ is definitely true asÂ
their would 998 times 1's present in the series , So, the result will definitely bigger than 497.
Now,Â
$$14\frac{3}{4}+5\frac{1}{4}-2\frac{1}{2}=\frac{59+21-10}{4}=\frac{70}{4}=17.50\ .$$
And, $$11\frac{1}{8}+12\frac{3}{8}-7\frac{1}{4}=\frac{89+99-29}{8}=\frac{159}{8}=19.875\ .$$
So, II is not correct .
A is correct choice.
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