Consider the following expression: (1 + x) ^n. A) Use the Binomial Theorem to find the first four terms of this polynomial. B) Why is 1 + nx a good approximation of this expression when x is less than 1?

Given:

The expression: (1 + x) ^n

The Binomial Theorem is used to predict the products of a binomial raised to a certain power, n, without multiplying the terms one by one.

The following formula is used:

(a + b) ^n = nCk * a^ (n-k) * b^k

we have (1 + x) ^n,

where a = 1

b = x

let n = 4

First term, k = 1

4C1 = 4

first term: 4 * (1^ (4-1)) * x^1

Therefore, the first term is 4x. Do the same for the next three terms.

2nd term: k = 2

3rd term: k = 3

4th term: k = 4