Finding a term in a binomial expnasion

In summary, the conversation discusses finding the term in the expansion of (x-(2/x^2))^14 that is of the form constant/x. The solution is found by setting up the equation 14-r=2r-1 and solving for r, which results in r=5.
  • #1
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Homework Statement



Find the term in the expansion of (x-(2/x^2))^14 which is of the form constant/x.



The Attempt at a Solution


I have worked out the general expression. (14|r) x^14-r * (-2/x^2)^r

However I can only work out this problem by trial and error. I know that in this case r=5, however I didn't solve it by equation. What equation would I need to construct to get this answer r=5? I know that for the answer to be constant/x the power of x on the denominator can only be 1 greater than the power of x on the numerator.

How do I construct an equation with r to solve this?

Thanks
 
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  • #2
(-2)/(x^2)^r=(-2)/x^(2r). And, just as you said, 14-r should be one less than 2r. Can you set up the equation from there?
 
  • #3
haha oh dear. bit of a facepalm moment.

14-r=2r-1

solve to get r=5

I never thought of just putting 2r-1.

Thanks for getting that out of me!
 

What is a binomial expansion?

A binomial expansion is a mathematical process that involves raising a binomial expression (x + y) to a certain power. The result is a polynomial expression with terms that consist of combinations of the variables x and y.

Why is it important to find a specific term in a binomial expansion?

Finding a specific term in a binomial expansion can be helpful in simplifying and solving mathematical problems involving binomial expressions. It can also be used to determine the coefficients and exponents in the expansion.

How do you find a specific term in a binomial expansion?

To find a specific term in a binomial expansion, you can use the binomial theorem or the Pascal's triangle method. Both methods involve determining the coefficients and exponents of the variables in the term you are looking for.

What is the binomial theorem?

The binomial theorem is a formula that allows us to expand a binomial expression raised to a certain power. It states that the coefficient of a term in the expansion is equal to the corresponding entry in Pascal's triangle, multiplied by the appropriate powers of the variables.

Can you give an example of finding a specific term in a binomial expansion?

Sure, let's say we want to find the 4th term in the expansion of (2x + 3)^5. We can use the formula (nCr)x^(n-r)y^r, where n is the power, r is the term we are looking for, and nCr represents the entry in Pascal's triangle. In this case, n = 5, r = 4, and nCr = 5C4 = 5. So, the 4th term would be 5(2x)^(5-4)(3)^4, which simplifies to 5(2x)(81) = 810x.

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