  We study weak-coupling perturbation expansions for the ground-state energy of
the Hamiltonian with the generalized spiked harmonic oscillator potential V(x)
= Bx^2 + A/x^2 + lambda/x^alpha, and also for the bottoms of the angular
momentum subspaces labelled by ell = 0,1,2 ..., in N-dimensions corresponding
to the spiked harmonic oscillator potential: V(x) = x^2 + lambda/x^alpha, where
alpha is a real positive parameter. A method of Znojil is then applied to
obtain closed form expressions for the sums of some infinite series whose terms
involve ratios and products of gamma functions.
