Question 1068010
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Sum the following term of progression to the last term, logx, logx^2 logx^3.... logx^120
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What are your terms ???


{{{log((x^120))}}}  or  {{{(log((x)))^120}}} ???


USE PARENTHESES.



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<U>Comment from student</U>: Log(x^120)
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<U>My response</U>:  OK, now I can complete the solution.


<pre>
  log(x) + log(x^2) +  log(x^3) + . . . . +  log(x^120) = 

= log(x) + 2*log(x) + 3*log(x) + . . . . + 120*log(x) =

= log(x)*(1 + 2 + 3 + . . . . + 120) = {{{log(x)*((120*121)/2)}}} = 7260*log(x).
</pre>

Solved.


About this sum, 1 + 2 + 3 + . . . . + 120, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</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 online textbook under the topic <U>"Arithmetic progressions"</U>.