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kaxThegeometric power seriesk0kaxconverges forx<1 and is equal toxa1 .Let g be sequence in (0, 1) that converges to 1. The matrix based onconvergent infinite geometric series defined as = (1- . Wedenote this matrix by Mgand name it geometric matrix. Mg is asequence to sequence mapping. When a matrix Mgis applied to asequence x, we get a new sequence Mgwhose nth term is given by: