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Exercise 14: Calculate the limit  .
Solution:

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Method 1:

The numerator of sequence is sequence of geometric with quotient q = 0,2 5 (-1, 1), so the limit is  0. The denominator of sequence is diverge ( + K ), so  the denominator is mianownik diverge ( + K ), the sequence converges to 0.

Method 2: The sequence is the product of two sequences: one geometric sequence c_n = (0,2)ⁿ with quotient q = 0,5 5 (-1, 1), so the limit is  0 and the sequence . Calculate the limit of sequence d_n we divide numerator and denominator by the highest power of variable n appearing in the denominator, We divide numerator and denominator by n³, we have