When can the binomial theorem be used?

The theorem and its generalizations can be used to prove results and solve problems in combinatorics, algebra, calculus, and many other areas of mathematics. The binomial theorem also helps explore probability in an organized way: A friend says that she will flip a coin 5 times.

What is the index of binomial?

The theorem states that “the total number of terms in the expansion is one more than the index. For example, in the expansion of (a + b)n, the number of terms is n+1 whereas the index of (a + b)n is n, where n be any positive integer.

Is binomial theorem valid for negative power?

The binomial theorem for positive integer exponents n can be generalized to negative integer exponents. This gives rise to several familiar Maclaurin series with numerous applications in calculus and other areas of mathematics.

What is range of validity?

Validity tells you how useful your experimental results are; a validity coefficient is a gauge of how strong (or weak) that “usefulness” factor is. In general, validity coefficients range from zero to . 50, where 0 is a weak validity and . 50 is moderate validity.

Why binomial theorem is used?

The binomial theorem is used heavily in Statistical and Probability Analyses. It is so much useful as our economy depends on Statistical and Probability Analyses. In higher mathematics and calculation, the Binomial Theorem is used in finding roots of equations in higher powers.

Is binomial theorem for rational index?

Putting x = 0 gives a 1 = n. an=n(n−1)(n−2)… (n−r+1)r!

Does binomial theorem work for non integers?

I finally figured out that you could differentiate xn and get nxn−1 using the derivative quotient, but that required doing binomial expansion for non-integer values. The most I can find with binomial expansion is the first, second, last, and second to last terms.