Y by Adventure10, chessgocube, megarnie, fluff_E, Mango247, bjump, buddyram, cubres, and 3 other users
Let
be an integer. Let
,
, ...,
be positive real numbers such that
Show that
,
,
are side lengths of a triangle for all
,
,
with
.




![\[n^2 + 1 > \left( t_1 + t_2 + \cdots + t_n \right) \left( \frac{1}{t_1} + \frac{1}{t_2} + \cdots + \frac{1}{t_n} \right).\]](http://latex.artofproblemsolving.com/1/a/b/1ab410ebc17d9f6c38a3e7ae0f6efa955ffddfd3.png)







This post has been edited 2 times. Last edited by djmathman, Jun 27, 2015, 11:54 PM