- #1
sludger13
- 83
- 0
I'm looking for a proof of a validity of the inequation:
[itex](n-1)\sum_{i=1}^{n}x_{i}^{2}\neq 2\sum_{i=1,j=1,j<i}^{n}x_{i}x_{j}[/itex]
Assumptions:
[itex]n\geq 2[/itex]
[itex]\exists (i,j),x_{i}\neq x_{j}[/itex]
[itex]i=1,...,n[/itex]
[itex]j=1,...,n[/itex]
I have no idea how to prove those non-trivial expressions.
[itex](n-1)\sum_{i=1}^{n}x_{i}^{2}\neq 2\sum_{i=1,j=1,j<i}^{n}x_{i}x_{j}[/itex]
Assumptions:
[itex]n\geq 2[/itex]
[itex]\exists (i,j),x_{i}\neq x_{j}[/itex]
[itex]i=1,...,n[/itex]
[itex]j=1,...,n[/itex]
I have no idea how to prove those non-trivial expressions.