http://i39.tinypic.com/u92sw.jpg
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It should be clear that the set is bounded below, since no no negative number is in the set, and every negative is less than everything in the set. This is because x_0 is defined to be 2, and every other term is just the sum of positive terms.
Therefore -2, for example is a lower bound.
To see if there is an upper bound, we should simplify a little, after a little algebraic manipulation
x_n = 17/3(x_n-1)^2 + 2x_n-1.
Well the first term is 17/(some number); it may be a large number or it many be a small term, but the important thing is it is nonnegative.
The second term is the important one 2x_n-1. This is 2 times the last term.
Thus each term is 2 times the last term + some positive number.
This means that the set has no upper bound.
Therefore -2, for example is a lower bound.
To see if there is an upper bound, we should simplify a little, after a little algebraic manipulation
x_n = 17/3(x_n-1)^2 + 2x_n-1.
Well the first term is 17/(some number); it may be a large number or it many be a small term, but the important thing is it is nonnegative.
The second term is the important one 2x_n-1. This is 2 times the last term.
Thus each term is 2 times the last term + some positive number.
This means that the set has no upper bound.
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It only has a lower bound, which is 31/12.
It has no upper bound
It has no upper bound