| The sequences {Fn} and {Ln} are well known as the Fibonacci and Lucas sequences respectively. In this thesis, we present in detail several methods to evaluate certain types of series involving reciprocals of Fibonacci and Lucas sequences, named Fibonacci and Lucas series. Some new results are achieved and introduced.;In addition, we study some interesting properties of the Jacobi elliptic functions sn(z), cn(z), and dn(z). We also discuss some properties of the Lambert series. These properties are essential for evaluation of Fibonacci and Lucas series.;Moreover, we will evaluate series involving the reciprocals of the Horadam sequence {Wn} and its special cases including Fibonacci, Lucas, Pell, and Fermat series. |
