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Exercise 15: Calculate the limit  .
Solution: 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

 

The sequence (0,1)ⁿ is geometric sequence with quotient
q = 0.5 5 (-1, 1), so it  converges to 0.

Using the theorem (  If is a real number, then),  we can write