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Exercise 14: Calculate the limit  .
Solution page 3:

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Method 3:

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

In the numerator we have the product of two sequences: the geometric sequence with quotient q = 0,2 5 (-1, 1), so the limit is  0 and the sequence converges to 0, so the limie of numerator is 0 * 0 = 0. In the denominator we use the theorem   ( If is a real number, then)

Thus