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.
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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
 =  =  .
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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):
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