2.4.6. Let

{x_(n)}

be a sequence. Suppose that there is an

ain(0,1)

such that\

|x_(n+1)-x_(n)|

\ for all

ninN

. Prove that

x_(n)->x

for some

xinR

.

4.6. Let {xn} be a sequence. Suppose that there is an a(0,1) such that xn+1xnan for all nN. Prove that xnx for some xR