document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184312>Question 1184312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the co-efficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E10+ ALIGN=MIDDLE  ALT=\"+x%5E10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the following expressions:<BR>\n" );
document.write( "(A) 1 + (1 + x) + (1 + x)^2 + ... + (1 + x)^20<BR>\n" );
document.write( "(B) (1 + x)^2 + (1 + x)^3 + (1 + x)^4 + (1 + x)^5 + .... + (1 + x)^10<BR>\n" );
document.write( "[Note: Here ^ means power] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814842 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (A)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+%281+%2B+x%29+%2B+%281+%2B+x%29%5E2+%2B+%22...%22+%2B+%281+%2B+x%29%5E20++=+%28%281+%2B+%281+%2B+x%29+%2B+%281+%2B+x%29%5E2+%2B+%22...%22+%2B+%281+%2B+x%29%5E20+%29%28%281%2Bx%29+-+1%29%29%2F%28%281%2Bx%29+-+1%29+=+%28%281%2Bx%29%5E21-1%29%2Fx ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28sum%28%28matrix%282%2C1%2C21%2Ck%29%29%2Ax%5E%2821-k%29%2C+k=0%2C21%29+-+1%29%2Fx ALIGN=MIDDLE  ALT=\"+%28sum%28%28matrix%282%2C1%2C21%2Ck%29%29%2Ax%5E%2821-k%29%2C+k=0%2C21%29+-+1%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E21+%2B+21x%5E20+%2B+%22...%22+%2B+%28matrix%282%2C1%2C21%2C9%29%29%2Ax%5E12+%2B+%28matrix%282%2C1%2C21%2C10%29%29%2Ax%5E11+%2B+%28matrix%282%2C1%2C21%2C11%29%29%2Ax%5E10+%2B+%22...%22+%2B21x%29%2Fx%0D%0A%0D%0A%0D%0A+=++x%5E20+%2B+21x%5E19+%2B+%22...%22+%2B+%28matrix%282%2C1%2C21%2C9%29%29%2Ax%5E11+%2B+highlight%28%28matrix%282%2C1%2C21%2C10%29%29%29%2Ax%5E10+%2B+%28matrix%282%2C1%2C21%2C11%29%29%2Ax%5E9+%2B+%22...%22+%2B21%0D%0A+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(B) This should be more manageable than (A).  Note that the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10 ALIGN=MIDDLE  ALT=\"x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > appears in the last term of the expression only, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bx%29%5E10 ALIGN=MIDDLE  ALT=\"%281%2Bx%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Therefore the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E10 ALIGN=MIDDLE  ALT=\"x%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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