Lacsaps Fractions Theory essays

Lacsap's Fractions Theory essays 2.Deriving general expression of Numerator 3 3.Deriving general expression of denominator 10 4.Validating the general expression 14 5.FINDING ADDITIONAL ROWS USING GENERAL EXPRESSION 19 Lacsap's fractions are based upon Pascal's triangle. The general triangle's rule is "Starting with1/1 at the top, the numerator (top number) is increased by one each step to downward right, and the denominator (bottom number) is increases by one each step to the downward left. Each fraction on the inside thereby has the numerator of the fraction to its upper-right, and the denominator of the fraction to its upper-left." So basically, going to the right, the denominator increases but if we go to the left, the numerator increases, both by one. The purpose of this assignment is to examine a set of fractions presented in a symmetrical pyramid, and generate a general formula for the fractions with respect to the row and element number after considering the first five rows. Well be finding a general statement for En(r) of the Lacsaps fractions, where En(r) denotes the fraction, n stands for the nth row and r stands for the number in the row starting with r = 0. I am going to use MS-Office as a technological tool. Lets represent each of the Lacsaps fraction in the following form: where, n denotes the row number and r denotes the element number in the row starting from 0. Let N(n) represents the numerator of the fraction and denotes the denominator. Before trying to find a general statement, we should change all the 1s into fractions based on the numerator because all the numerators of each row are the same. Our pattern should look like this after doing so. Now we can separate the numerator from the denominator and work with it separately to get two equations which will be combined later on. 2. Deriving general expression of Numerator Since all the numerators have the same numerical value in the row, we wou...