show that there is no positive integer n, for which_/(n-1)+_/(n+1) is rational.
Answers & Comments
BeUnknown
Square the above expression to gt 2n + sqrt(n^2-1). Since gap between two squares at most 1 (that too for the case of 0 and 1 only) n =1 is the only integer which "may" give a rational answer for the concerned expression.
But on putting the value n=1, we get that the concerned expression becomes sqrt(2) which is irrational. Hence there is no natural number meeting our needs.
Answers & Comments
But on putting the value n=1, we get that the concerned expression becomes sqrt(2) which is irrational. Hence there is no natural number meeting our needs.