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MATHEMATICS Convergent sequence

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Exercise 23: Calculate the limit  for x5§
Solution:

Please, note that  ,so we have the following limit .

The function  f(x) = x2 + 2x + 1 takes only positive values, as  f(x) = x2 + 2x + 1= (x + 1)2 > 0. Thus, the limit

.

We divide numerator and denominator of the sequence of geometric with the highest quotient appearing in the denominator.  We divide numerator and denominator by 9n.
We have


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