Summation of reciprocal which involve products of terms from generalized Fibonacci sequences. II (Q2735226)

Let \(\{W_n\}\) denote the sequence defined by \(W_n=pW_{n-1}+W_{n-2}\), \(W_0=a, W_1=b\). The author investigates the infinite sums NEWLINE\[NEWLINE S_{k, m}=\sum_{n=1}^\infty {\overline{W}_{k(n+m)}\over W_{kn}W_{k(n+m)}W_{k(n+2m)}} NEWLINE\]NEWLINE and NEWLINE\[NEWLINE T_{k, m}=\sum_{n=1}^\infty {1\over W_{kn}W_{k(n+m)}W_{k(n+2m)}W_{k(n+3m)}}, NEWLINE\]NEWLINE where \(\{\overline{W}_n\}\) is a companion sequence of \(\{W_n\}\). Values of some infinite sums involving Fibonacci and Lucas numbers are obtained as an application. Part I of this paper was published in [Fibonacci Q. 38, 294-298 (2000; Zbl 0962.11009)].