Question: Project problems. Please submit your full solution toP4, taking into account thefeedback you have received.P4. Suppose that a0b0>0 are given real numbers. For n0, let

Project problems. Please submit your full solution toP4, taking into account thefeedback you have received.P4. Suppose that a0b0>0 are given real numbers. For n0, let an+1=an+bn2 and letbn+1=anbn2. The overall goal isto show that limnan=limnbn.(a) Show thatx+y2xy2for all x,y0.(b) Experiment with different values a0 and b0. Based on the experiments, make a conjectureabout inequalities between an,bn,an+1, and bn+1.(c) Prove the inequalities you conjectured in part (b).(d) Show that limnan and limnbnL and M.limnan+1=limnan=L and the limit laws, show that L=M.

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