Suppose the sequence, a(n+1) = 1/2 (an + 7/an) with a1 = 2
Show that a^2n > 7
So i've said a^2(n+1) > 7
a^(n+1) - 7 = 1/4((an^2 + 7)^2/4a^2)
And then I hit a wall, any thoughts?
The function for [for is ...] is illustrated here...
There is an 'attractive fixed point' at . Any will produce a sequence converging at but, because is [see 'red line'...] for and for , any will produce a sequence for ...