SOLUTION: Sum the following term of progression to the last term, logx, logx^2 logx^3.... logx^120

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Question 1068010: Sum the following term of progression to the last term, logx, logx^2 logx^3.... logx^120
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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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%28%28x%5E120%29%29 or %28log%28%28x%29%29%29%5E120 ???

USE PARENTHESES.


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

  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%28x%29%2A%28%28120%2A121%29%2F2%29 = 7260*log(x).

Solved.

About this sum, 1 + 2 + 3 + . . . . + 120, see the lessons
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
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 lessons are the part of this online textbook under the topic "Arithmetic progressions".