Food for thought

Scary sum Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Suggestion

Evaluate the sum $\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \dotsb + \frac{1}{\sqrt{15} + \sqrt{16}}.$

(You might want to use a calculator to get an estimate of the answer, but in order to get the exact answer you will have to do it by hand!)

The denominators are quite scary. Maybe we can make them nicer somehow.

Things like $\sqrt{5}+\sqrt{6}$ make me think of the difference of two squares….