document.write( "Question 1116740: Please help me with this problem: Resolve into infinite series $\"ax%2F%28a-x%29\"$ \r
\n" ); document.write( "\n" ); document.write( "I can't show how I tried on this problem because it is very complicated! I did try several times though.\r
\n" ); document.write( "\n" ); document.write( "This is the answer from my key book: x+x^2/a+x^3/a+x^4/a,ect., to infinity\r
\n" ); document.write( "\n" ); document.write( "I don't understand how the fractions are able to keep repeating. When I worked the problem I got as far as x+x^2/a, but no farther.
\n" ); document.write( "I appreciate any help you can offer! \n" ); document.write( "

Algebra.Com's Answer #731660 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The formula in your post is written   I N C O R R E C T L Y.\r
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\n" ); document.write( "\n" ); document.write( "            The correct formula is   T H I S:\r
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\n" ); document.write( "\n" ); document.write( "             $\"ax%2F%28a-x%29\"$ = $\"x\"$ + $\"x%5E2%2Fa\"$ + $\"x%5E3%2Fa%5E2\"$ + $\"x%5E4%2Fa%5E3\"$ + . . . ,   ect.,   to infinity.\r
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\n" ); document.write( "It is not difficult to prove it   //   if you know the formula for the sum of an infinite geometric series . . . \r
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document.write( " =  = .\r\n" );
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document.write( "The very right fraction    is the sum of an infinite geometric progression with the first term of \"1\" and the common ratio of :\r\n" );
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document.write( " =  1 +  +  +  + . . .      (1)\r\n" );
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document.write( "Now multiply both sides of (1) by x, and you will get the required solution\r\n" );
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document.write( " = x +  +  +  + . . .\r\n" );
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document.write( "QED.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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