document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346582>Question 346582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello I seem to be stuck at this problem.<BR>\n" );
document.write( "I'm not to sure how to write it as the n and n-1 are subscripts.<BR>\n" );
document.write( "Show that an = Sn – Sn-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247769 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=247769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use brackets, or you can use parentheses.<BR>\n" );
document.write( "parentheses are easier to write.<BR>\n" );
document.write( "brackets are more formal.<BR>\n" );
document.write( "i'll use parentheses.\r<BR>\n" );
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document.write( "formula is a(n) = S(n) - S(n-1) where () means sub.\r<BR>\n" );
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document.write( "In general, S(n) = a(1) + a(2) + ........ a(n-1) + a(n)\r<BR>\n" );
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document.write( "In general S(n-1) = a(1) + a(2) + ........a (n-1)\r<BR>\n" );
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document.write( "If you subtract one from the other, you are left with a(n) because all of the a's from a(0) to a(n-1) cancel out.\r<BR>\n" );
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document.write( "a(1) - a(1) = 0<BR>\n" );
document.write( "a(2) - a(2) = 0<BR>\n" );
document.write( "a(n-1) - a(n-1) = 0<BR>\n" );
document.write( "a(n) - 0 = a(n)\r<BR>\n" );
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document.write( "nothing left but a(n).\r<BR>\n" );
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document.write( "there's a more formal proof that can be done, but it's more complicated to go through and not worth the effort unless you absolutely have to do it that way.\r<BR>\n" );
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document.write( "for your purposes, this shows that it's true and should be sufficient.\r<BR>\n" );
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document.write( "you can then cover with examples:\r<BR>\n" );
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document.write( "let a1 = 5 and let d = 7 (d = common difference in arithmetic sequence).\r<BR>\n" );
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document.write( "s(7) = 5 + 12 + 19 + 26 + 33 + 40 + 47 = 182\r<BR>\n" );
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document.write( "s(8) = 5 + 12 + 19 + 26 + 33 + 40 + 47 + 54 = 236\r<BR>\n" );
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document.write( "s(8) - s(7) = 236 - 182 = 54\r<BR>\n" );
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document.write( " </SPAN>\n" );
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