Pick the correct option regarding $Q$.
$Q=\frac{1}{100}+\frac{1}{101}+\cdots+\frac{1}{1000}$ Pick one option:
- $Q>1\qquad$ 2. $Q\leq \frac{1}{3}\qquad$ 3. $\frac{1}{3}
4. $\frac{2}{3}
My approach :
$Q = \frac{1}{100}+\frac{1}{101}+\cdots+\frac{1}{1000} > \frac{1}{1000}+\frac{1}{1000}+\cdots+\frac{1}{1000} = \frac{901}{1000}$ $\implies \frac{1}{100}+\frac{1}{101}+\cdots+\frac{1}{1000} > \frac{9}{10}$
So, $Q > 1$. Option 1 is correct.
Now, my question is: can this be proved with some other approach?