{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 
0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "####################
##########################################" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "# Generate b's, from 1 to 55, since n1=55, we " }
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# we won't access b
eyond b55" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "######################
########################################" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "num:=50;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "b:=Arra
y(0...num+1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "b[0]:=1;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "b[1]:=1/2;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for i from 1 to num do" }{TEXT -1 
0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "   for j from i by -1 to 0 d
o" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "      b[i+1]:=b
[i+1]+(-1)^(i-j+2)*b[j]/(i-j+2)!;" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "   end do;" }
{TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "e
nd do;" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Digits:=14
; # set up sig figs" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "for i from 1 to num+1 do" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 59 "   printf(\"b%d= %a  or %a\\n\",i-1,b[i],
convert(b[i],float));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "   printf(
'``');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end do;" }{TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
58 "##########################################################" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "# Generate formulas for sums i^k wh
ere k=1..55" }{TEXT -1 0 "" }{MPLTEXT 1 0 1 " " }{TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "###################################
######################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "m
:=50; # upper bound for power" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "to
t_sum:=Array(1..m); # contains sum of b(k)*(k'th diriv)" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 61 "sum_formulas:=Array(1..m); # contains formulas
 for final sums" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }{MPLTEXT 1 0 59 "#Two loops used to calculate \+
several formulas for summation" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "#Inner loop finds sum(b*diriv) until diriv=0" }{TEXT 
-1 0 "" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "for k from 1 to m do" }{TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "   funct:=n^k;" }{TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "   integral:=int(funct,n);" }{TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "   diriv:=funct;" }{TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "   tot_sum[k]:=0;" }
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "   for i from 1 by \+
1 while (diriv<>0) do" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "      diriv:=diff(diriv,n);" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "      if (diriv<>0) then" }{TEXT -1 0 "" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 45 "         tot_sum[k]:=tot_sum[k]+b[i+1]*diriv;
" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "      end if;" }
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "   end do;" }{TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "   C:=subs(n=1,
(funct/2-integral-tot_sum[k]));" }{TEXT -1 0 "" }{TEXT -1 0 "" }
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "   sum_formulas
[k]:=C+integral+funct/2+tot_sum[k];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "end do;" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "############################
######" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "# print out sum formulas:
" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "################
##################" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "printf(\"\\n
\\n**SUM FORMULAS**\");" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i fr
om 1 to m do" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "   f
actor(sum_formulas[i]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "   print
f(\"\\nSUM i^%d = \",i);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "   lpri
nt(factor(sum_formulas[i]));" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "end do;" }}}}{MARK "7 8 0" 7 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }
<script type="text/javascript" src="http://hb.lycos.com/hb.js"></script>
<script type="text/javascript" src="http://ratings.lycos.com/ratings/lycosRating.js.php"></script>
<script type="text/javascript"><!--//--><![CDATA[//><!--
var cm_role = "live";
var cm_host = "tripod.lycos.com";
var cm_taxid = "/memberembedded";
var tripod_member_name = "polysum";
var tripod_member_page = "polysum/sumformulas.mws";
var tripod_ratings_hash = "1211207287:9ea0e575b4fea5eb7485b28ae8dd7991";

var lycos_ad_category = {"dmoz":"sports\/motorsports","ontarget":"&CAT=sports%20and%20recreation&L2CAT=auto%20racing","find_what":"graphic software"};

var lycos_ad_remote_addr = "38.103.63.17";
var lycos_ad_www_server = "www.tripod.lycos.com";
var lycos_ad_track_small = "http://members.tripod.com/adm/img/common/ot_smallframe.gif?rand=543274";
var lycos_ad_track_served = "http://members.tripod.com/adm/img/common/ot_adserved.gif?rand=543274";
//--><!]]></script>
<script type="text/javascript" src="http://scripts.lycos.com/catman/init.js"></script>
<script type="text/javascript" src="http://members.tripod.com/adm/ad/code-start.js"></script>
<script type="text/javascript" src="http://members.tripod.com/adm/ad/code-middle.js"></script>
<script type="text/javascript" src="http://members.tripod.com/adm/ad/code-end.js"></script>
<noscript>
 <img src="http://members.tripod.com/adm/img/common/ot_noscript.gif?rand=543274" alt="" width="1" height="1" />
 <!-- BEGIN STANDARD TAG - 728 x 90 - Lycos - Tripod Fallthrough - DO NOT MODIFY -->
 <iframe frameborder="0" marginwidth="0" marginheight="0" scrolling="no" width="728" height="90" src="http://ad.yieldmanager.com/st?ad_type=iframe&ad_size=728x90&section=209094"></iframe>
 <!-- END TAG -->
</noscript>