document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=579911>Question 579911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the limits of the sequences.\r<BR>\n" );
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document.write( "an= cos(n*pi /2)\r<BR>\n" );
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document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371255 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=+cos%28pi%2F2%29=0 ALIGN=MIDDLE  ALT=\"a%5B1%5D=+cos%28pi%2F2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=+cos%282%2Api%2F2%29=cos%28pi%29=-1 ALIGN=MIDDLE  ALT=\"a%5B2%5D=+cos%282%2Api%2F2%29=cos%28pi%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=+cos%283%2Api%2F2%29+=0 ALIGN=MIDDLE  ALT=\"a%5B3%5D=+cos%283%2Api%2F2%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=+cos%284%2Api%2F2%29=cos%282%2Api%29=1 ALIGN=MIDDLE  ALT=\"a%5B4%5D=+cos%284%2Api%2F2%29=cos%282%2Api%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and it repeats from then on because cosine is periodic with a period of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D=0 ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D=a%5B2%5D=-1 ALIGN=MIDDLE  ALT=\"a%5B6%5D=a%5B2%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and so on. In general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B4%5D=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B4%5D=a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%3Ca%5Bn%5D=cos%28n%2Api%2F2%29+%3C=1 ALIGN=MIDDLE  ALT=\"-1%3Ca%5Bn%5D=cos%28n%2Api%2F2%29+%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not converge. It just keeps flip-flopping between 1 and -1, hitting 0 in between. There is no limit.<BR>\n" );
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