What is the greatest coefficient in binomial expansion?

Greatest coefficient in a binomial expansion.

• When n is even, the greatest coefficient is nCn/2​.
• when n is odd, the greatest coefficient is nCn−1/2​ornCn+1/2​ ; these two coefficients being equal.

What is the middle term in a binomial expansion?

Binomial Theorem Formula – Middle Term. When you are trying to expand (a + b)^n and ‘n’ is an even number, then (n + 1) will be an odd number. For example, if you are expanding (x + y)^2 , then the middle term will be the ( \frac {2}{2} + 1) = 2nd term.

How do you find the greatest term in an expansion?

To determine the numerically greatest term in the expansion of (a + x)n, where n is a positive integer. Note : {((n+1)/r) – 1} must be positive since n > r. Thus Tr+1 will be the greatest term if, r has the greatest value as per the equation (1).

What is the greatest coefficient of a polynomial?

The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading term is the term with the highest power, and its coefficient is called the leading coefficient.

How do you find the middle term of an arithmetic sequence?

An arithmetic series is the expression with summation of the terms inn AP sequence. If there even number of terms we shall find two middle terms m1=n2,m2=n2+1.

Which term is 2x 3y 12?

8th term
8th term.

Why is the coefficient of the term with the greatest degree also the leading coefficient of the polynomial?

We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first.

What is the leading term of the polynomial function?

In a polynomial, the leading term is the term with the highest power of x. For example, the leading term of 7+x−3×2 is −3×2. The leading coefficient of a polynomial is the coefficient of the leading term.