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Nov 16, 2016 at 5:43 comment added Pietro Majer As usually done: square both sides of the relation for the $x_n$, then call $x_n^2=Y_n$, getting a recursion for $Y_n$, which is the one you already have for $y_n$, with the same initial conditions, so $y_n=Y_n$ for all $n$.
Nov 16, 2016 at 5:31 comment added T. Amdeberhan Can you show how?
Nov 16, 2016 at 5:21 history answered Pietro Majer CC BY-SA 3.0