# How do you derive (1 + 9)^n from the second step?

## Question:

How do you derive (1 + 9){eq}^n {/eq} from the second step?

## Binomial Series:

A binomial series is an algebraic expression. A binomial series is valid when the *n* is a positive integer. In this question, we will use the binomial expansion to calculate the second step of the expansion {eq}(1+9)^n. {/eq}

## Answer and Explanation:

The binomial series is defined as:

{eq}(a+b)^n = a^n + na^{n-1}b + \dfrac{n(n-1)}{2!}a^{n-2}b^2 + .... + b^n {/eq}

Putting {eq}a = 1 \ , \ b = 9 {/eq} in the above equation, we get:

{eq}(1+9)^n = 1^n + n\times 1^{n-1}9 + \dfrac{n(n-1)}{2!}\times 1^{n-2}\times 9^2 + .... + 9^n {/eq}

So, the second step is {eq}9\times n. {/eq}

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

Get access to this video and our entire Q&A library

#### Related to this Question

What is the probability of obtaining twelve tails...

In a recent study 35 % of people surveyed indicate...

If 90 % of married women claim that their...

From past experience, it is known 90% of...

Suppose that the chance that a prospective...

Use an appropriate binomial series and integration...

A company is manufacturing highway emergency...

Find the binomial series for the function (1 + 4...

Find the geometric power series that represents...

Use the Binomial Theorem to find the coefficient...

Find the coefficient of x^{10} in the expansion of...

Determine the coefficient of x^{11} in the...

#### Explore our homework questions and answers library

Browse
by subject