SOLUTION: Please help me solve this: Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.

Algebra.Com
Question 1141509: Please help me solve this:
Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.
Found 3 solutions by Alan3354, ikleyn, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
If you know the "term formula" use that.
----------
If you don't know it and just want someone to give you the answer, what does that accomplish?

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The binomial expansion is this formula


     =  +  +  +  + . . . +  + 


In our case,  n = 20,  x = ab,  y = -1,  therefore, the common term of the binomial expansion in our case is  


    , k = 0, 1, 2, 3, 4, 5, . . . 


Then the 5-th term is at k = 4 


     =  = .

--------------

If you want to see other similar solved problems and to learn the subject wider and deeper,  look into the lesson
    - Solved problems on binomial coefficients
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic
"Binomial expansion, binomial coefficients, Pascal's triangle".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Please help me solve this:
Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.
BINOMIAL EXPANSION term formula: , where r = term number, or 5, and n = 20.

We then get: 5th term of 

             5th term of 

             5th term of 

             5th term of  

RELATED QUESTIONS


I am having trouble understanding how to solve this question. Please help me.

Find the  (answered by josgarithmetic,MathTherapy)

Please help me solve this problem: 
Find the eight term in the expansion of (a + b)10

 (answered by nerdybill)

Find the constant term in the expansion of (-3x^5 + 4/x)^36. 
Please help me solve this,  (answered by Theo)

a. use factorial notation to write the coefficient of the fifth term in the expansion of... (answered by stanbon)

find the fifth term in the binomial expansion of (2x -... (answered by Edwin McCravy)

Find the fifth term in the binomial expansion of... (answered by MathLover1)

Find the fifth term in the expansion of... (answered by amarjeeth123)

 The first term of an arithmetic sequence is 1.  The fifth term is 6.  Find the 2009th... (answered by bucky)

 Can you please help me find the sixth term in the expansion of... (answered by stanbon)