document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198089>Question 1198089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the terms of the series ∑n r=1 log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400.[ans: S20 = 146.78, n = 34] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831641 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28log%28%285r%29%29%2Cr=1%2Cn%29+=+log%28%285%2A1%29%29%2Blog%28%285%2A2%29%29%2Blog%28%285%2A3%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2Blog%28%285%2An%29%29 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=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+log%28%285%2A1%29%29%2Blog%28%285%2A2%29%29%2Blog%28%285%2A3%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2Blog%28%285%2A20%29%29 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=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+%28log%28%285%29%29%2Blog%28%281%29%29%29%2B%28log%28%285%29%29%2Blog%28%282%29%29%29%2B%28log%28%285%29%29%2Blog%28%283%29%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2B%28log%28%285%29%29%2Blog%28%2820%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule that log(A*B) = log(A)+log(B)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+%28log%28%285%29%29%2Blog%28%285%29%29%2Blog%28%285%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2Blog%28%285%29%29%29%2B%28log%28%281%29%29%2Blog%28%282%29%29%2Blog%28%283%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2Blog%28%2820%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > See note1 below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+20%2Alog%28%285%29%29%2B%28log%28%281%29%29%2Blog%28%282%29%29%2Blog%28%283%29%29%2Bmatrix%281%2C1%2C%22...%22%29%2Blog%28%2820%29%29%29 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=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+20%2Alog%28%285%29%29%2Blog%28%28matrix%281%2C1%2C%221%2A2%2A3%2A...%2A20%22%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > See note2 below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+32.365524703598 ALIGN=MIDDLE  ALT=\"sum%28log%28%285r%29%29%2Cr=1%2Cn=20%29+=+32.365524703598\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximate\r<BR>\n" );
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document.write( "It seems strange that your teacher is getting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B20%5D+=+146.78 ALIGN=MIDDLE  ALT=\"S%5B20%5D+=+146.78\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I have a feeling I might be mis-interpreting the given expression.\r<BR>\n" );
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document.write( "Footnotes:<ul><li>note1: The first parenthesis grouping has 20 copies of \"log(5)\" added together, which leads to 20*log(5) in the next line.</li><li>note2: Use the rule log(A)+log(B) = log(A*B). The log(1*2*3*...*20) leads to log(20!) where the exclamation mark indicates factorial.</li></ul><BR>\n" );
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