document.write( "Question 1183173: Hello this is a mathematical induction prove question I need help with.
\n" ); document.write( "
\n" ); document.write( "1. Show that, for every positive integer n:
\n" ); document.write( "1 + 2 + 2^2 + 2^3 + … + 2^(n-1) = 2^n - 1 \n" ); document.write( "
Algebra.Com's Answer #813358 by robertb(5830)\"\" \"About 
You can put this solution on YOUR website!
This is an alternative solution.\r
\n" ); document.write( "\n" ); document.write( "It is easy to see by direct multiplication that \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(1-x)*(1 + x + x^2 + x^3 +...+ x^(n-1)) = 1 - x^n.
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "If you let x = 2 in the above equation, you will get \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(-1)*(1 + 2 + 2^2 + 2^3 +...+ 2^(n-1)) = 1-2^n\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This implies then that \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1 + 2 + 2^2 + 2^3 +...+ 2^(n-1) = 2^n -1,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "after multiplying both sides of the equation by -1.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );