document.write( "Question 608591: I have a problem that I simply cannot solve. I have to put this series into summation notation, but I can't find the explicit formula! The series is\r
\n" ); document.write( "\n" ); document.write( "1 + 1/4 + 1/9 + 1/16 + 1/25\r
\n" ); document.write( "\n" ); document.write( "How do I even find the common difference in a series like that? \n" ); document.write( "

Algebra.Com's Answer #383320 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
I have a problem that I simply cannot solve. I have to put this series into summation notation, but I can't find the explicit formula! The series is\r
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\n" ); document.write( "\n" ); document.write( "How do I even find the common difference in a series like that?
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document.write( "That is neither an arithmetic nor a geometric series.  You are not asked\r\n" );
document.write( "to find the sum of the series.  You are only asked to find the summation\r\n" );
document.write( "series.  What you want is this:\r\n" );
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document.write( "Re-write the series \r\n" );
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document.write( "1 +  +  +  +  \r\n" );
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document.write( "as this:\r\n" );
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document.write( " +  +  +  + \r\n" );
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document.write( "That can be written this way:\r\n" );
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document.write( "k is the \"dummy\" variable, sometimes called the \"index\".\r\n" );
document.write( "You can use another letter besides k if you like.  The ∑\r\n" );
document.write( "is the Greek letter \"sigma\" for \"S\" which stands for \"SUM\" \r\n" );
document.write( "At the bottom of the ∑ is k=1 and the top is 5.  At the\r\n" );
document.write( "right of the ∑ you see a formula .  This means\r\n" );
document.write( "to start out by substituting 1 for k in the formula \r\n" );
document.write( "getting  which is 1.  You write that down as the first\r\n" );
document.write( "term.\r\n" );
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document.write( "So you have 1\r\n" );
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document.write( "Then you substitute k=2 in that formula \r\n" );
document.write( "getting  which is , so you put a + after the\r\n" );
document.write( "1 and write that after it:\r\n" );
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document.write( "Now you have 1 + \r\n" );
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document.write( "Then you substitute k=3 in that formula \r\n" );
document.write( "getting  which is , so you put a + and write \r\n" );
document.write( "that after it:\r\n" );
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document.write( "Now you have 1 +  + \r\n" );
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document.write( "Then you substitute k=4 in that formula \r\n" );
document.write( "getting  which is , so you put a + and write \r\n" );
document.write( "that after it:\r\n" );
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document.write( "Now you have 1 +  +  + \r\n" );
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document.write( "Then you substitute k=5 in that formula \r\n" );
document.write( "getting  which is , so you put a + and write \r\n" );
document.write( "that after it:\r\n" );
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document.write( "Now you have 1 +  +  + \r\n" );
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document.write( "And you have finished because there is a 5 at the top of the ∑\r\n" );
document.write( "which tells you when to stop.\r\n" );
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document.write( "But all you were asked to give as an answer is\r\n" );
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document.write( "Edwin

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