PATTERN OF BINOMIAL EXPANSION

INTRODUCTIONA binomial expression is an expression which has two terms, such as (a+b). The

expression of the form (a+b)n is called a binomial expression. The binomial expansion that is raised to some power can be obtained quickly using the Binomial Theorem. When the binomial is raised to a whole number powers, the coefficients of the terms in the expansion form a pattern.

Binomial expression can be exhibited many patterns. Each expansion has one more term than the power on the binomial. The sum of the exponents in each term in the expansion is the same as the power on the binomial. The coefficients can be formed in Pascal’s Triangle because it is a symmetrical pattern.

Theoretically speaking, Pascal’s Triangle can be used to obtain the expansion of (a+b )n for any positive integral value of n. However, this becomes impractical for large

values of n since getting the relevant row of the triangle would be troublesome and inefficient.

Pascal’s Triangle is essential to the discussion of binomial expansion because, as it turns out, the number in Pascal’s Triangle is the coefficients of the terms in the binomial expansion of the form (a+b)n. We will also investigate the relation between the binomial coefficient and the Pascal’s Triangle.

In this assignment, we are required to investigate how the binomial theorem to help us in expanding the binomial expansion quickly. We are also required to investigate the pattern of the terms in the expansion.

The binomial expansion of (a+b)n can be obtained in the general formula. The

general formula for the binomial expansion of (1+x )n also can be obtained by substitute a=1 and b=x in the pattern of the coefficients of the terms.

Lastly, we have to find an approximate for the Euler’s number, e. It is approximately equal to 2.71828… and it is the limit of ¿ as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series.