Question 87
Prove that
$$
\sqrt{1 + \frac{1}{n^2} + \frac{1}{(n+1)^2}}
$$
is rational for every positive integer $n$.
$$
\sqrt{1 + \frac{1}{n^2} + \frac{1}{(n+1)^2}}
$$
is rational for every positive integer $n$.
MathNet 2016-part-01 — 184 problems (EN–VI) Question 87
Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)