SOLUTION: find the sixteenth term of (2-1/x)^18

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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): You can put this solution on YOUR website!


I suspect the other tutor answered the wrong problem, since the question is not posed well....

"find the sixteenth term IN THE EXPANSION OF of (2-1/x)^18"





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The above answer is a correction of my original response below.

The 16th term in the expansion is the one with the (-1/x) term to the 15th power, not the 16th.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
find the sixteenth term of (2-1/x)^18.
~~~~~~~~~~~~~~~~~~~


            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): You can put this solution on YOUR website!
find the sixteenth term of (2-1/x)^18
16th term of:

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