Note on THE l-TRANSLATIVITY OF Matrix Based on Convergent Infinite Geometric Series - Lemma, Mulatu; Fuller, Keith (IJRDO -JOURNAL OF MATHEMATICS, 2017)
The infinite Geometric Series is a series of the form . 0   k k ax The geometric power series   k0 k ax converges for x <1 and is equal to x a 1 . Let g be sequence in (0, 1) that converges to 1. The matrix based on convergent infinite geometric series defined as = (1- . We denote this matrix by M g and name it geometric matrix. M g is a sequence to sequence mapping. When a matrix M g is applied to a sequence x, we get a new sequence M g whose nth term is given by: