document.write( "Question 1158359: prove that (n 0) + (n 1) + (n 2) + ... + (n k) = 2^n is true using mathematical induction\r
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Algebra.Com's Answer #781305 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " There is another way and another method to prove it,\r
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document.write( "Use the binomial formula\r\n" );
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document.write( "     = 1 +  +  + +  + . . . +  + .\r\n" );
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document.write( "Now plug in x= 1 into this formula.  You will get\r\n" );
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document.write( "     = 1 +  +  + +  + . . . +  + 1,\r\n" );
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document.write( "and the proof is completed.\r\n" );
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document.write( "Those who saw this proof at least once in their life, will never forget it . . . \r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Remarkable identities for Binomial Coefficients\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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