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</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的部=
分和</span><span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1026" type=3D"#=
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style=3D'width:27pt;height:33.75pt' o:ole=3D"">
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<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
026"
DrawAspect=3D"Content" ObjectID=3D"_1220424309">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的极=
限存在,则称该级数=
5910;敛,并称此极限为ಪ=
3;数的和。在</span><span
lang=3DEN-US>Matlab</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>中,=
用于级数求和的命令=
6159;</span><span
lang=3DEN-US>symsum()</span><span style=3D'font-family:SimSun;mso-ascii-fon=
t-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,该=
命令的应用格式为:</s=
pan></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.0=
pt;
mso-char-indent-count:2.0'><span lang=3DEN-US><span
style=3D'mso-spacerun:yes'> =
</span>symsum(comiterm,v,a,b)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>其中:</span><span
lang=3DEN-US>comiterm</span><span style=3D'font-family:SimSun;mso-ascii-fon=
t-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>为级=
数的通项表达式,</span><span
lang=3DEN-US>v</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>是通项中&#=
30340;求和变量,</span><span
lang=3DEN-US>a</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>和</span><span lang=3DEN-US>=
b</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>分别为求和变量=
的起点和终点。如果</s=
pan><span
lang=3DEN-US>a</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>,</span><span lang=3DEN-US>=
b</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>缺省,则</span><span lang=3DEN-U=
S>v</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>从</span><span lang=3DEN-US>0</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>变到</span><span lang=3DEN-US>v-1</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>,如果</span><span lang=3DEN-US>v</spa=
n><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>也缺省,则系统=
对</span><span
lang=3DEN-US>comiterm</span><span style=3D'font-family:SimSun;mso-ascii-fon=
t-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>中的=
默认变量求和。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>例</span><span lang=3DEN-US>1</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>:求级数</span><span lang=3DEN-U=
S><sub><!--[if gte vml 1]><v:shape
id=3D"_x0000_i1027" type=3D"#_x0000_t75" style=3D'width:66.75pt;height:33.=
75pt'
o:ole=3D"">
<v:imagedata src=3D"sy12.files/image005.wmz" o:title=3D""/>
</v:shape><![endif]--><![if !vml]><img width=3D89 height=3D45
src=3D"sy12.files/image006.gif" v:shapes=3D"_x0000_i1027"><![endif]></sub><=
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<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
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</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
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src=3D"sy12.files/image008.gif" v:shapes=3D"_x0000_i1028"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
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</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的和=
。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>解:利用</span><span
lang=3DEN-US>Matlab</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>函数=
</span><span
lang=3DEN-US>symsum</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>设计=
如下程序:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>clear</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>syms n</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>f1=3D(2*n-1)/2^n;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>f2=3D1/(n*(2*n+1));</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I1=3Dsymsum(f1,n,1,inf)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I2=3Dsymsum(f2,n,1,inf)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>运行结果为:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I1 =3D3</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I2 =3D2-2*log(2)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>本例是收敛的情=
况,如果发散,则求=
4471;的和为</span><span
lang=3DEN-US>inf</span><span style=3D'font-family:SimSun;mso-ascii-font-fam=
ily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,因=
此,本方法就可以同=
6102;用来解决求和问题ࡴ=
4;收敛性问题。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>例</span><span lang=3DEN-US>2</span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>:求级数</span><span lang=3DEN-U=
S><sub><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><![if !vml]><img width=3D84 height=3D45
src=3D"sy12.files/image010.gif" v:shapes=3D"_x0000_i1029"><![endif]></sub><=
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<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
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</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>,</span><=
span
lang=3DEN-US><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1030" type=3D"#=
_x0000_t75"
style=3D'width:87pt;height:35.25pt' o:ole=3D"">
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</v:shape><![endif]--><![if !vml]><img width=3D116 height=3D47
src=3D"sy12.files/image012.gif" v:shapes=3D"_x0000_i1030"><![endif]></sub><=
!--[if gte mso 9]><xml>
<o:OLEObject Type=3D"Embed" ProgID=3D"Equation.DSMT4" ShapeID=3D"_x0000_i1=
030"
DrawAspect=3D"Content" ObjectID=3D"_1220424313">
</o:OLEObject>
</xml><![endif]--></span><span style=3D'font-family:SimSun;mso-ascii-font-f=
amily:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>的和=
。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>解:</span><span
lang=3DEN-US>Matlab</span><span style=3D'font-family:SimSun;mso-ascii-font-=
family:
"Times New Roman";mso-hansi-font-family:"Times New Roman"'>程序=
如下:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>clear</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>syms n x</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>f3=3Dsin(x)/n^2;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>f4=3D(-1)^(n-1)*x^n/n;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I3=3Dsymsum(f3,n,1,inf)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I4=3Dsymsum(f4,n,1,inf)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>运行结果为:</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>I3 =3D1/6*sin(x)*pi^2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
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