document.write( "Question 962542: Prove by induction:\r
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Algebra.Com's Answer #589850 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"1%2Ba%2Ba%5E2%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2Ba%5E%28n-1%29=%28a%5En-1%29%2F%28a-1%29\"\r\n" );
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document.write( "Prove true for n=1: (There is only one term)\r\n" );
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document.write( "\"1=a%5E%281-1%29\"\r\n" );
document.write( "\"1=a%5E0\"\r\n" );
document.write( "\"1=1\"\r\n" );
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document.write( "So it is true for n=1\r\n" );
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document.write( "Assume it is true for all n ≤ k\r\n" );
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document.write( "\"1%2Ba%2Ba%5E2%2B%22%22%2A%22%22%2A%22%22%2A%22%22%2Ba%5E%28k-1%29=%28a%5Ek-1%29%2F%28a-1%29\"\r\n" );
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document.write( "Add \"a%5Ek\" to both sides\r\n" );
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document.write( "Simplifying the right side:\r\n" );
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document.write( "\"%28a%5Ek-1%29%2F%28a-1%29%2Ba%5Ek\"\r\n" );
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document.write( "\"%28a%5Ek-1%29%2F%28a-1%29%2Ba%5Ek%2F1\"\r\n" );
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document.write( "\"%28a%5Ek-1%29%2F%28a-1%29%2Ba%5Ek%2A%28a-1%29%2F%28a-1%29\"\r\n" );
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document.write( "\"%28%28a%5Ek-1%29%2Ba%5Ek%2A%28a-1%29%29%2F%28a-1%29\"\r\n" );
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document.write( "\"%28a%5Ek-1%2Ba%5E%28k%2B1%29-a%5Ek%29%2F%28a-1%29\" \r\n" );
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document.write( "\"%28cross%28a%5Ek%29-1%2Ba%5E%28k%2B1%29-cross%28a%5Ek%29%29%2F%28a-1%29\" \r\n" );
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document.write( "\"%28-1%2Ba%5E%28k%2B1%29%29%2F%28a-1%29\"\r\n" );
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document.write( "\"%28a%5E%28k%2B1%29-1%29%2F%28a-1%29\"\r\n" );
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document.write( "And that is exactly what you would get if you substitute\r\n" );
document.write( "n=k+1 in \"%28a%5En-1%29%2F%28a-1%29\".\r\n" );
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document.write( "So the formula is proved.\r\n" );
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document.write( "Edwin
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