Abstract:
The original solution of Problem B-1177 in the problem section of this journal. It was acquired to prove that the limits of special sequences whose terms are expressed by sums and fractions of powers of the Fibonacci and Lucas numbers with positive integer exponent p have the given values. These values are expressed by a sum of the Lucas numbers and a difference of the Fibonacci numbers with the indices equal to p and 2p. The proof is done by using of the Binet formula for the generalized Fibonacci numbers, whose special cases are the common Fibonacci and Lucas numbers.