Let-x-r-r-1-n-be-n-positive-real-numbers-Show-That-x-1-1-x-1-2-x-2-1-x-1-2-x-2-2-x-n-1-x-1-2-x-2-2-x-n-2-lt-n-

Question Number 198311 by York12 last updated on 17/Oct/23

L e t {x_{r}}_{r = 1}^{n} b e n p o s i t i v e r e a l n u m b e r s S h o w T h a t :

\frac{x_{1}}{1 + x_{1}^{2}} + \frac{x_{2}}{1 + x_{1}^{2} + x_{2}^{2}} + \dots + \frac{x_{n}}{1 + x_{1}^{2} + x_{2}^{2} + \dots + x_{n}^{2}} < \sqrt{n}