sorry, not sure which subforum this should go to.
Sequence u1, u2, u3,... is know to converge to the limit m and is such that
a) find the value of m.
b) it is given that . by first writing in terms of , and considering , prove by induction that for all positive integers n.
i substitute m, giving
solving this gives
how do i immediately know whether it is -1 or 3 that it converges to? i know i can draw a graph of against , and draw a line of y=x, and based on the gradient of the curve determine which it converges to. but i believe im not supposed to do that, this topic is only induction. and also this is a short question which probably carries very little marks. there must be some direct and quick way to immediately see which it converges to?
i proved that it is valid for n=1.
i assumed that it is valid for n=k.
expressing in terms of ,
since it is assumed ,
this is where my problem starts. i can't show from here that
how? in fact what i get is . theres this , which shouldn't be if i were to prove this.