The sequence is the product of two sequences the geometric sequence c_n = (0,5)ⁿ and the . And using the theorm ( If is a real number, then ) the sequence d_n converges to 0.

the sequence c_n = (0,5)ⁿ is geometric with quotient q = 0,5 5 (-1, 1), so the limit is  0.

Using the theorem: If  a sequence has limit  a, and a sequence has limit b ( where ), then , we have

Method 2: When calculating the limit of the sequence is enough to note that the numerator is a sequence of geometric with quotient q = 0.5 5 (-1, 1), so it  converges to 0, and the denominator is diverge ( + K ), therefore the sequence converges to 0.