please friends can u help me with the question below
Q. If T is contraction, show that T^n (n\inN) is a contraction. If T^n is a contraction for all n>1, show that T need not be a contraction.
Thanks
For the first question, prove by induction that $\displaystyle d(T^n(x),T^n(y))\leq\alpha ^n d(x,y) \forall x,y\in X$ if $\displaystyle \forall x,y\in X, d(Tx,Ty)\leq \alpha d(x,y)$.