A level math SS.

• Jia Xun

  29 Apr 12, 02:29

  Hi,i was wondering if anyone can help me with this question from the A level tys,N2007/P1/Q9 of H2 math.I don't know how to start off apart from using GC for the first part.Welcome any relevant explanations,thanks.:)

• wee_ws

  29 Apr 12, 07:16

  Hi,

    This must-know question is a classic problem of recurrences. Many schools adapt the question for their tests and exams after that.

    For part (ii):

    1. Use this fact:

    as n -> infinity, x_{n + 1} and x_{n} both approach the limit L.

    2. Substitute x_{n + 1} and x_{n} with L and rewrite the equation to look like the one you solved in (i).

    3. The conclusion is then obvious.

    For part (iv):

    1. Use the consideration given.

    2. Use the given graph to make the two conclusions.

    For part (v):

    1. Note that the 1st result in part (iv) demonstrates the convergence of a decreasing sequence.

    2. Note that the 2nd result in part (iv) shows the convergence of an increasing sequence.

    3. Consider, for part (iii), whether alpha < x_1 < beta when you apply the results.

    Thanks.

  Cheers,
  Wen Shih