Question

The sum of the series $\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\dots \dots +\frac{1}{\sqrt{224}+\sqrt{225}}$ is:

• A. $15-\sqrt{3}$
• B. $\sqrt{15}-2$
• C. 12
• D. None of these

Answer 1

The correct option is A $15-\sqrt{3}$

You can easily see that for the first term sum of the series is $2-\sqrt{3}$, for 2 terms we have the sum as $\sqrt{5}-\sqrt{3}$ and so on. For the given series of 120 terms the sum would be $\sqrt{225}-\sqrt{3}=15-\sqrt{3}$. Option (a) is correct.