What is a so that LIM(x->inf) ( (x+a)/(x-a) ) ^ x = e ? (Which I saw him present today, 7-30-22, on youtube)
I argue straightaway that a = 1/2. We know that 1) LIM(x->inf) ( (1 + (1/x))^x ) = e.
But 1 + (1/x) can also be written as (x+1)/x. So, if we let y = x + 1/2 above, and use a = 1/2:
then LIM(x->inf) ( (x+1/2)/(x-1/2) ) ^ x becomes LIM(y->inf) ( (y+1)/y ) ^ (y-1/2).
As y->inf, y-1/2 becomes y. This is just 1) with 'y' instead of 'x'.
How do I submit this to bprp channel, of which I'm a member? - 0over0 (Jack Ritter)