document.write( "Question 827159: Prove than sum(1/(r^2),r=1,n)is greater than or equal to 2- (1/n) for n is greater than or equal to 1. \r
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Algebra.Com's Answer #498816 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "This is not true!\r\n" );
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document.write( "Although equality holds for n=1:\r\n" );
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document.write( "It isn't true for n=2 or greater, for when n=2\r\n" );
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document.write( "yet\r\n" );
document.write( ",  holds but not \r\n" );
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document.write( "And when n=3\r\n" );
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document.write( "yet\r\n" );
document.write( ", again  holds but not .\r\n" );
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document.write( "Euler proved in 1735 that the the sum on the left approaches the irrational\r\n" );
document.write( "number  = 1.6449340668482264... and it is an increasing function, so it\r\n" );
document.write( "is always less that .\r\n" );
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document.write( "The expression on the right is also increasing, and approaches 2.  But\r\n" );
document.write( "beginning with the third term it is already larger than the left side can \r\n" );
document.write( "ever be!\r\n" );
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document.write( "Edwin

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