The notation used to denote a binomial coefficient is or .
Let's first consider the expansion using the Binomial Theorem of the following parentheses.
(x+y)^3= 1* x^3+ 3* x^2y+ 3* xy^2+ 1* y^3
On the right-hand side, the numbers that precede the variables are called binomial coefficients. We can use the following notation to represent them.
(x+y)^3= _3C_0* x^3+ _3C_1* x^2y+ _3C_2* xy^2+ _3C_3* y^3
In general, the symbol _nC_r represent the coefficient of the rth term (we count the terms from 0 to n) in the expansion of (x+y)^n. Sometimes, another symbol is used to denote the binomial coefficients.
(x+y)^3= (_0^3)* x^3+ (_1^3)* x^2y+ (_2^3)* xy^2+ (_3^3)* y^3
Similarly, (_r^n) represents the rth term in the expansion of (x+y)^n. Now, let's complete the statement!
The notation used to denote a binomial coefficient is _nC_r or (_r^n) .
