document.write( "Question 1141231: please help me with this mathematical induction 1/2^1+1/2^2+1/2^3+....+1/2^n =1-1/2^n. \n" ); document.write( "

Algebra.Com's Answer #761801 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
please help me with this mathematical induction 1/2^1+1/2^2+1/2^3+....+1/2^n =1-1/2^n.
\n" ); document.write( "------------------
\n" ); document.write( "please help me by proving this statement using mathematical induction $\"1%2F2%5E1%2B1%2F2%5E2%2B1%2F2%5E3+\"$ + ... + $\"+1%2F2%5En+=+1-1%2F2%5En\"$ .
\r
\n" ); document.write( "\n" ); document.write( "


\n" );
document.write( "n=1:     Ok for n=1.  This is the base-case. \r
\n" );
document.write( "\n" );
document.write( "Assume it is true for n=k:  that is,   + ... +  =   holds for n=k.   This is the hypothesis statement.\r
\n" );
document.write( "\n" );
document.write( "Now look at the case n=k+1:\r
\n" );
document.write( "\n" );
document.write( " + ... +  \r
\n" );
document.write( "\n" );
document.write( "If we exclude the very last term for a second, the remainder is the same case as n=k, which we can re-write by applying the hypothesis:\r
\n" );
document.write( "\n" );
document.write( "=  + \r
\n" );
document.write( "\n" );
document.write( "Putting everthing over a common denominator (step-by-step):
\n" );
document.write( "= \r
\n" );
document.write( "\n" );
document.write( "= \r
\n" );
document.write( "\n" );
document.write( "= \r
\n" );
document.write( "\n" );
document.write( "Dividing the numerator by the denominator:
\n" );
document.write( "=    DONE (the hypothesis leads to truth for n=k+1)\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( "

\n" );