document.write( "Question 1109139: For what values of n will the infinite series (2n-1)+(2n-1)^2+...+(2n-1)^i+... have a finite value \n" ); document.write( "

Algebra.Com's Answer #724168 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "The sum of an infinite geometric progression converges if and only if the common ratio is less than 1 by the modulus.  In your case it means\r\n" );
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document.write( "|2n -1| < 1,   or,  equivalently,\r\n" );
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document.write( "The solution to the last inequality are all those \"n\" that are remoted less than   from , i.e.\r\n" );
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document.write( "    0 < n < 1.\r\n" );
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document.write( "Or, in the interval notation,  those \"n\" that belong to the interval (0,1)   (the ends are not included !).\r\n" );
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