How to Verify the 5th Term of the Binomial Expansion of (3-2/x)^9?

In summary, a binomial series is a mathematical expression used to expand powers of a binomial expression. To check if a series is binomial, it must follow the form (a+b)^n, and this is important for determining its properties and identifying patterns. Common errors when checking binomial series include incorrectly expanding or counting terms. A series cannot be both binomial and not binomial, as it must strictly follow the (a+b)^n form to be considered binomial.
  • #1
donniemateno
45
0
hi there I am abit stuck here. i got a q saying :
in binomial expansion of (3-2/x)^9 find the 5th term using the general term of the binomial expansion and check your answer

(3-2/x)^9

used formula

=N!/(n-r)!r! * A^(n-r) * b ^ r

r= 4
a= 3
b= - 2/x
n=9

got a answer of -489888/x^4

How do i go about checking my answer??
 
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  • #2
My answer is like yours, but without the negative sign.
 

1. What is a binomial series?

A binomial series is a mathematical expression that represents the expansion of powers of a binomial expression, such as (a+b)^n. It is used to simplify complex algebraic expressions and to calculate probabilities in statistics.

2. How do you check if a series is binomial?

A series is considered binomial if it follows the form (a+b)^n, where a and b are constants and n is a non-negative integer. To check if a series is binomial, you can expand it and see if it matches this form.

3. What is the purpose of checking a binomial series?

Checking a binomial series allows us to determine its properties, such as the coefficients and terms, which can be used in various mathematical calculations. It also helps us identify any patterns or relationships within the series.

4. What are some common errors when checking binomial series?

Some common errors when checking binomial series include incorrectly expanding the series, forgetting to include all terms, or miscounting the powers of the variables. It is important to double check your work and use algebraic rules correctly to avoid these errors.

5. Can a series be both binomial and not binomial?

No, a series can either be binomial or not binomial. In order for a series to be considered binomial, it must follow the specific form of (a+b)^n. If any of the terms or coefficients do not match this form, then the series is not binomial.

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