document.write( "Question 1193591: Find the sum of this series that is not arithmetic or geometric,
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\n" ); document.write( "\n" ); document.write( "can someone help, a few of us have been trying to figure this out, our teacher said its solvable but I don't even know where to start, thankyou \n" ); document.write( "

Algebra.Com's Answer #825639 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "1+2+4+5+7+8....+95+97+98
\n" ); document.write( "can someone help, a few of us have been trying to figure this out,
\n" ); document.write( "our teacher said its solvable but I don't even know where to start, thankyou
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\n" ); document.write( "\n" ); document.write( "The major problem with your post is that it is BAD STYLE presenting a Math task.\r
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\n" ); document.write( "\n" ); document.write( "Actually, in your post the problem is not posed as a Math problem.\r
\n" ); document.write( "\n" ); document.write( "The reader should guess what this sequence/series is.\r
\n" ); document.write( "\n" ); document.write( "When a reader should guess what the author wants to say, it is just not a Math problem.\r
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\n" ); document.write( "\n" ); document.write( "So, I will re-formulate it to present it in a way, as it SHOULD be presented.\r
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document.write( "    |  In the sequence of 99 first natural numbers from 1 to 99 inclusive,   |\r\n" );
document.write( "    |  each third term is removed. Find the sum of remaining numbers.        |\r\n" );
document.write( "    +------------------------------------------------------------------------+\r\n" );
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\n" ); document.write( "\n" ); document.write( " Now it is normal Math entertainment problem.\r
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document.write( "For the solution, the reader should know that the sum of the first n natural numbers is .\r\n" );
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document.write( "It is one of the basic facts about arithmetic progressions.\r\n" );
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document.write( "If you don't know it, you may derive this formula, but then the problem itself is not an entertainment - it is just \r\n" );
document.write( "full size study piece of knowledge.\r\n" );
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document.write( "So, to keep this style of entertainment problem, I will assume that you know this formula.\r\n" );
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document.write( "If so, then the entire problem is two easy steps.\r\n" );
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document.write( "First, the sum of natural numbers from 1 to 99 is   =  = 99*50 = 4950.\r\n" );
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document.write( "From it, we should subtract the sum of all \"removed\" terms, which is\r\n" );
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document.write( "    3 + 6 + 9 + . . . + 96 + 99 = 3*(1 + 2 + 3 + . . . + 32 + 33).\r\n" );
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document.write( "In the parentheses, we have the sum of the first 33 natural numbers, which is   = 33*17 = 561.\r\n" );
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document.write( "Now your  ANSWER  is this difference  4950 - 3*561 = 3267.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved   (keeping the style of an entertainment problem).\r
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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Also, did your mother or other relatives teach you to thank those who help you ?

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