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Recursive Sequence Given Recursive Formula and Seed

Please see the attached file for the fully formatted problems.

Please show me how to solve question 1 part d of lecture two in the "non elegant" way.

I'd like you to "work backwards from what you want to prove until you arrive at a true formula" l
like in part C of question 1.

I've provided the solutions so you can see what I mean.


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1. In this problem, we will see that a certain recursive sequence converges to the value . Given the recursive formula and seed

d) show that if , then .

Note: (Algebra of Inequality)
We manipulate the inequality the same way as we do with the equation, except for one extra rule. The rule states that if we multiply both sides by a negative value, the inequality sign must change to the opposite. For example, consider the following inequality,
It can be seen that if we multiply both sides by -2, this inequality will be
We keep both terms and on their original sides, but we change only the inequality sign from less-than sign (<) to greater-than sign (>). ...

Solution Summary

A recursive sequence is investigated given a recursive formula and seed. The solution is detailed and well presented.