In this paper, we study the solutions of the second-order generalized difference equation having the form ofwhereThen we provide applications on 2( ) and c 0( ) .
In this article, the authors discuss 2() and c 0() solutions of the second order generalized difference equation 2 u(k) + f (k, u(k)) = 0, k ∈ [a, ∞), a > 0 and we prove the condition for non existence of non-trivial solution where u(k) = u(k +)-u(k) for > 0. Further we present some formulae and examples to find the values of finite and infinite series in number theory as application of .
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