document.write( "Question 1062031: Prove that\r
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Algebra.Com's Answer #676825 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Prove that\r\n" );
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document.write( "\"6%2F%28n%2B1%29+%3C=+6%2F%282n%2B1%29+%2Bsqrt%28sum%281%2Fk%5E2%2C+k=1%2Cn%29%29\" for \"n+%3E=+1\"\r\n" );
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document.write( "That will be true if and only if\r\n" );
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document.write( "\"6%2F%28n%2B1%29+-+6%2F%282n%2B1%29++%3C=+sqrt%28sum%281%2Fk%5E2%2C+k=1%2Cn%29%29\" for \"n+%3E=+1\"\r\n" );
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document.write( "Simplifying the expression on the left,\r\n" );
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document.write( "\"%286n%29%2F%28%28n%2B1%29%282n%2B1%29%29++%3C=+sqrt%28sum%281%2Fk%5E2%2C+k=1%2Cn%29%29\" for \"n+%3E=+1\"\r\n" );
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document.write( "The proof is immediate because the left side decreases as\r\n" );
document.write( "n gets larger and the right side increases as n gets larger,\r\n" );
document.write( "so the inequality will always hold for \"n+%3E=+1\".\r\n" );
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document.write( "Edwin

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