Matrix Based on the Second Derivative of Infinite Convergent Geometric Series

Abstract

The infinite Geometric Series is a series of the form ? ? ?0k kax , where a is a constant. The geometric power series ? ? ?0k kax converges for x <1 and is equal to x a ?1 . The Second Derivative of ? ? ?0k kax is ? ? ? ?? 2 2)1( k kxkak =? ? ? ?? 0 )1)(2( k kxkka Let t be sequence in (0,1) that converges to 1. The matrix based on second derivative of convergent infinite geometric series defined as