document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495865>Question 495865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use mathematical induction to prove the following:<BR>\n" );
document.write( "(a) For each natural number n <BR>\n" );
document.write( "with n > or equal to 2, 3^n > 1 + 2^n. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336245 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=336245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The base cases (n=1, 2) hold. For some n>2, if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3^n > 1 + 2^n\">, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3^{n+1} = 3(3^n)\">\r<BR>\n" );
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document.write( "from our original inequality, we establish\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3^{n+1} = 3(3^n) > 3(1+2^n)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  = 3 + 3(2^n) = (1 + 2^{n+1}) + (2 + 2^n)\">\r<BR>\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3^{n+1} > (1+2^{n+1})\"> and the induction is complete. </SPAN>\n" );
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