Question 1179417
.
Find the specified nth term in the expansion of the binomial.
(x - 10z)^7, n = 5
~~~~~~~~~~~~~~~


<pre>
They want you determine the 5-th term in the binomial expansion


    {{{(x-10z)^7}}} = {{{sum(C[7]^k*x^(7-k)*(-10z)^k, k=0,7)}}}.



     +------------------------------------------------------------------+
     |    The 5-th term  is  at  k=4  (be attentive and notice it:      |
     |    you should take k=4,  NOT  k=5 (!) --- BECAUSE the counter    |
     |           k goes from k = 0)  and is equal to                    |
     +------------------------------------------------------------------+



    {{{C[7]^4*x^3*(-10z)^4}}} = {{{((7*6*5)/(1*2*3))*x^3*10^4*z^4}}} = {{{350000x^3*z^4}}}.


So the 5-th term is  {{{350000x^3*z^4}}}.      <U>ANSWER</U>
</pre>

Solved.


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See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Binomial-Theorem.lesson>Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Remarkable-identities-for-Binomial-Coefficients.lesson>Remarkable identities for Binomial Coefficients</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/The-Pascal-triangle.lesson>The Pascal's triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Permutations/Solved-problems-on-binomial-coefficients.lesson>Solved problems on binomial coefficients</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic
"<U>Binomial expansion, binomial coefficients, Pascal's triangle</U>".



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.