Reciprocal sums of the terms of the higher order recursive sequences

Let p_i's be arbitrary reals for all 1<=i<=k. Higher order linear recursive sequence {u_n } with constant coefficients and arbitrary initials is defined by the recursion u_n=p_1 u_(n-1)+p_2 u_(n-2)+...+p_k u_(n-k) In this thesis, we obtain some results about partial reciprocal and alternating partial reciprocal sums of the terms of the sequence {u_n } given by ||(sum_(k=n)^(infinity) 1/u_(tk+r) )^(-1)|| and ||(sum_(k=n)^(infinity) (-1)^k/u_(tk+r) )^(-1)|| according to choice of initials and coefficients for arbitrary integers t and r with 0<=r