# Explain binomial series.

Several series are known as binomial series.

## Answer: It is the sum of infinite series in one variable expressed in terms of general positive integers that occur as coefficients in the binomial theorem.

See detailed description.

**Explanation: **

A binomial series is the Taylor Series (Introduced by Brook Taylor in 1715) for function f(x) = (1 + x)^{α}, where α ∈ C (set of arbitrary complex numbers in the form of a + bi, where 'a' is a real number and 'bi' is an imaginary unit to satisfy the equation).

It is the sum of infinite series in one variable expressed in terms of general positive integers that occur as coefficients in the binomial theorem.

The polynomial expansion of the binomial power (1 + x)^{n }can be expressed in the form of Pascal's Triangle.

For Example, the expansion of ( 1 + x )^{2 }will be

⇒ 1 (1)^{2 }(x)^{0 }+ 2 (1)^{1 }(x)^{1 }+ 1 (1)^{0 }(x)^{2}

### ⇒ (1)^{2 }+ 2 (1)(x) + (x)^{2}

⇒ 1 + 2x + x^{2}