document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184905>Question 184905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty adding positive odd integers. Please exlain in the simplest form (I have to present this to my teacher) the following question:<BR>\n" );
document.write( "1+3=4<BR>\n" );
document.write( "1+3+5=9<BR>\n" );
document.write( "1+3+5+7=16<BR>\n" );
document.write( "1+3+5+7+9=25<BR>\n" );
document.write( "what is the sum of 1+3+5+7+9+....+99? Why?<BR>\n" );
document.write( "I know I have to use (2n-1) but dont know how. Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138765 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1+3=4<BR>\n" );
document.write( "1+3+5=9<BR>\n" );
document.write( "1+3+5+7=16<BR>\n" );
document.write( "1+3+5+7+9=25<BR>\n" );
document.write( "what is the sum of 1+3+5+7+9+....+99? Why?<BR>\n" );
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document.write( "Comment: Every odd number can be written in the form 2n-1 where<BR>\n" );
document.write( "n is an integer.  So another way of writing your problems is as follows:<BR>\n" );
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document.write( "(2*1-1) + (2*2-1) = 2(1+2)-2 = 6-2 = 4<BR>\n" );
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document.write( "(2*1-1)+(2*2-1)+(2*3-1) = 2(1+2+3)-3 = 12-3 = 9<BR>\n" );
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document.write( "(2*1-1)+(2*2-1)+(2*3-1)+(2*4-1) = 2(1+2+3+4)-4 = 20-4 = 16<BR>\n" );
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document.write( "Are you seeing the pattern?<BR>\n" );
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document.write( "Now the last line: what is the sum of 1+3+5+7+9+....+99? Why?\r<BR>\n" );
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document.write( "The last term is 2n-1 = 99; Solve for n to get n = 50<BR>\n" );
document.write( "So the sum is 2(1+2+3+...+49+50)-50 = 2-50 = [50*51]-50<BR>\n" );
document.write( "= 50*50 = 2500<BR>\n" );
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document.write( "I hope that helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( "I am having difficulty adding positive odd integers. Please exlain in the simplest form (I have to present this to my teacher) the following question:<BR>\n" );
document.write( "1+3=4<BR>\n" );
document.write( "Ans: So, 1+3 = 4<BR>\n" );
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document.write( "1+3+5=9<BR>\n" );
document.write( "Ans: (1+5)+3 = 6+3 = 9<BR>\n" );
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document.write( "1+3+5+7=16<BR>\n" );
document.write( "Ans: (1+7)+(3+5) = 8+8 = 16<BR>\n" );
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document.write( "1+3+5+7+9=25<BR>\n" );
document.write( "Ans: (1+9) + (3+7) + 5 = 2*10 + 5 = 25<BR>\n" );
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document.write( "what is the sum of 1+3+5+7+9+....+99? Why?<BR>\n" );
document.write( "Ans: (1+99) + (3+97) + (5+95) + (7+93) + ....(49+51) = ?<BR>\n" );
document.write( "Do you see the pattern?<BR>\n" );
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document.write( "Another way to do it:<BR>\n" );
document.write( "1+3=4<BR>\n" );
document.write( "Ans: 1 is 2*1-1 ; 3 is 2*2-1 <BR>\n" );
document.write( "So 1+3 = 2*1-1 + 2*2-1 = (2*1+2*2)-1-1 = 2(1+2)-2 = 2*3-2= 6-2= 4<BR>\n" );
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document.write( "1+3+5=9<BR>\n" );
document.write( "1+3+5 = 2(1+2+3)-1-1-1 = 2(6)-3 = 9<BR>\n" );
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document.write( "1+3+5+7=16<BR>\n" );
document.write( "1+3+5+7 = 2(1+2+3+4)-4 = 20-4= 16<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "1+3+5+7+9=25<BR>\n" );
document.write( "= 2(1+2+3+4+5)-5=2*15-5 = 30-5=25<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "what is the sum of 1+3+5+7+9+....+99? Why?<BR>\n" );
document.write( "2(1+2+3+...+50)-50= 2*(50/2)*51)-50 = 2550-50 = 2500<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( "I know I have to use (2n-1) but dont know how. Please help!<BR>\n" );
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