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MATHEMATICS Convergent sequence

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Exercise 24: Find  .

Solution page 2:
  The sequence converges to 0, as it is geometric sequence  with quotient .

The sequence converges to 0, as the numerator  converges to 1, and the denominator is diverges. ( +K )

The sequence converges to 0, to prowe that the use of the two inequalities    and  . We have

. The sequence  converges to 0, and the sequence converges to 0, as the numerator  converges to -1, and the denominator is diverges. ( +K ). Using the theorem of three sequences we have that the sequence converges to 0.

( Theorem ( three sequences ):  If  for three sequences we have and , then )

Therefore

 


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