Assume that, for $n\ge1$,$$a_n=\sqrt{1+\left(1+\frac{1}{n}\right)^2 } +\sqrt{1+\left(1-\frac{1}{n}\right)^2 } $$
How to prove that
$$\frac{1}{a_1} +\frac{1}{a_2} +...+\frac{1}{a_{20}}$$ is an integer?
Assume that, for $n\ge1$,$$a_n=\sqrt{1+\left(1+\frac{1}{n}\right)^2 } +\sqrt{1+\left(1-\frac{1}{n}\right)^2 } $$
How to prove that
$$\frac{1}{a_1} +\frac{1}{a_2} +...+\frac{1}{a_{20}}$$ is an integer?