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document.write( "We show that it's true for n=1.\r\n" );
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document.write( "Then we find out what would happen if there were some positive integer k,\r\n" );
document.write( "for which it were true. If it were true for n = k, then we would have:\r\n" );
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document.write( "If that were true, we would be able to add 2k to both sides and\r\n" );
document.write( "it would still be true. Then we would have:\r\n" );
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document.write( "That is the original expression with k+1 substituted for n.\r\n" );
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document.write( "So if we could find a positive integer k so that the equation were true,\r\n" );
document.write( "then we would know that it would have to also be true for the next higher\r\n" );
document.write( "positive integer.\r\n" );
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document.write( "Now we DO have a positive integer k=1 so that the equation is true! That's\r\n" );
document.write( "because at the first we showed that it is true when n=k=1, so that means it\r\n" );
document.write( "is true for n=2. Now, the fact that it's true for n=2 shows that it's also\r\n" );
document.write( "true for n=3, and so on and on, through all the positive integers.\r\n" );
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document.write( "Edwin
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