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Question 1185059: find the sixteenth term of (2-1/x)^18
Found 4 solutions by Edwin McCravy, greenestamps, ikleyn, MathTherapy:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! find the sixteenth term of (2-1/x)^18
Get your scientific or graphing calculator and put this in:
{2-1/16)^18
Then press = or "enter". You will then see the answer, which is
148030.362
Takes a rocket scientist!
Answer by greenestamps(13198)  (Show Source):
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
find the sixteenth term of (2-1/x)^18.
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Each such problem HAS a TRAP. A L W A Y S.
In the given problem, the trap is that the 16-th term IS NOT THE TERM with  .
Read my solution below attewntively and consider it as a standard MANTRA to solve such problems.
Following this mantra will allow you to avoid similar traps in the future.
The binomial expansion is this formula
 =  +  +  +  + . . . +  + 
In our case, n = 18, a = 2, b = - , therefore, the common term of the binomial expansion in our case is
 , k = 0, 1, 2, 3, 4, 5, . . . , 17, 18.
Notice that k= 0 for the 1-st term; k= 1 for the 2-nd term, and so on. Then the 16-th term is at k = 15
 = -  = -  = -  .
ANSWER. The 16-th term is - .
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If you want to see many other similar solved problems and to learn the subject wider and deeper, then 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(10551)  (Show Source):
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