# Binomial Theorem - Determine n

• Schaus
My mistake!In summary, the conversation is discussing the determination of n in the expansion of (x-1/5)^n, where the sixth term is given as -1287/(3125)x^8. By setting the bases of both terms equal and using the control calculation for binomial coefficients, it is determined that n=13.
Schaus

## Homework Statement

The sixth term of the expansion of (x-1/5)n is -1287/(3125)x8. Determine n.

tk+1=nCkan-kbk

## The Attempt at a Solution

tk+1=nCkan-kbk
t5+1=nC5(x)n-5(-1/5)5
This is where I'm stuck. Do I sub in -1287/(3125)x8 to = t6? If so what do I do from here?
-1287/(3125)x8 = nC5(x)n-5(-1/5)5?
Any help is greatly appreciated!

You already wrote ##(-\frac{1}{5})^5=-\frac{1}{3125}## and ##x^{n-5}=x^8##, what is ##n## then? ##\binom{n}{5}## should only serve as a control calculation.

Schaus
So all I need is the x8 and xn-5?
Then bases are the same so - n-5 = 8 ----> n=3?

Schaus said:
So all I need is the x8 and xn-5?
Then bases are the same so - n-5 = 8 ----> n=3?
##3-5=8## ?

Schaus
Whoops! Sorry I meant to put n = 13!

## What is the Binomial Theorem?

The Binomial Theorem is a mathematical formula used to expand binomials, which are expressions with two terms, raised to a positive integer power. It states that the coefficient of each term in the expansion can be determined using the combination formula nCr, where n is the power and r is the position of the term.

## What is n in the Binomial Theorem?

n represents the power to which the binomial is raised. It is also referred to as the degree of the binomial. In the Binomial Theorem, n is used to determine the number of terms in the expansion and to calculate the coefficients of each term.

## How do you determine n in the Binomial Theorem?

To determine n in the Binomial Theorem, you can use the formula n = (a + b)^n, where a and b are the terms of the binomial and n is the power. Alternatively, you can count the number of terms in the expanded binomial, which will also give you the value of n.

## What is the significance of n in the Binomial Theorem?

n is significant in the Binomial Theorem because it determines the number of terms in the expansion and helps in calculating the coefficients of each term. It also allows for the generalization of the formula, making it applicable to any binomial raised to any positive integer power.

## Why is it important to understand how to determine n in the Binomial Theorem?

Understanding how to determine n in the Binomial Theorem is important because it allows you to expand and simplify binomial expressions, which is useful in many mathematical applications. It also helps in understanding the patterns and relationships between the coefficients in the expansion, which can be applied to other mathematical concepts.

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