document.write( "Question 1146981: The n^th term, tn of a series:5/6+19/36+65/216+....... is given by Tn=a(1/2)^n+b(1/3)^n: find the values of a and b
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Algebra.Com's Answer #768301 by ikleyn(52874) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "It means that \r\n" );
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document.write( "     +  =       (1)    (at n= 1)\r\n" );
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document.write( "     +  =      (2)    (at n= 2)\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  =        (1')  \r\n" );
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document.write( "     +  =       (2') \r\n" );
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document.write( "Now your task is to solve the system (1'), (2') for unknown \"a\" and \"b\".\r\n" );
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document.write( "First step, divide by 2 all the terms in equation (1');  keep equation (2') as is.\r\n" );
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document.write( "     +  =        (3)  \r\n" );
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document.write( "     +  =        (4) \r\n" );
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document.write( "Next step subtract equation (4) from equation (3).  You will get then\r\n" );
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document.write( "                      = ,   or\r\n" );
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document.write( "                      =  = \r\n" );
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document.write( "which implies  b = -2.\r\n" );
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document.write( "Then from equation (1) you can find \"a\".\r\n" );
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document.write( "The rest is just arithmetic, which I leave to you to complete on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you still have questions, then let me know.\r
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