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한명수

Posted at 2012-01-14 17:08:04

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장재영 선생님의 답글입니다.   )자연수n에 대하여 집합 <OBJECT style="WIDTH: 346px; HEIGHT: 23px; TOP: 23px; LEFT: 26px" class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=346 align=absMiddle height=23><PARAM NAME="_cx" VALUE="9154"><PARAM NAME="_cy" VALUE="608"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/77.6`5.6/12,[1]{{A}_{n}`equal`{*(x,y)`vbar`y`gt`2x, y`leq`x`plus`n, x와y는 자연수 }}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 원소의 개수를 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=18 align=absMiddle height=24><PARAM NAME="_cx" VALUE="476"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/4.3`5.6/12,[1]{{a}_{n}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이라고 할 때, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=24 align=absMiddle height=24><PARAM NAME="_cx" VALUE="635"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/5.8`5.6/12,[1]{{a}_{10}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 값을 구하시오. (풀이) <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=41 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1084"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.2`4.3/12,[1]{x`equal`1}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이면 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=82 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2169"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/18.6`4.3/12,[1]{2`lt`y`leq`11}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=25 align=absMiddle height=24><PARAM NAME="_cx" VALUE="661"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/6`5.6/12,[1]{{A}_{10}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 에 속하는 원소는 9개. <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=41 align=absMiddle height=18><PARAM NAME="_cx" VALUE="1084"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/9.2`4.3/12,[1]{x`equal`2}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이면 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=83 align=absMiddle height=18><PARAM NAME="_cx" VALUE="2196"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/18.6`4.3/12,[1]{4`lt`y`leq`12}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이므로 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=25 align=absMiddle height=24><PARAM NAME="_cx" VALUE="661"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/6`5.6/12,[1]{{A}_{10}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 에 속하는 원소는 8개.   같은 방법으로 생각하면 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=170 align=absMiddle height=24><PARAM NAME="_cx" VALUE="4497"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/38.5`5.6/12,[1]{{a}_{10}`equal`9`plus`8`plus`hdot3`plus`1`equal`45}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>.   2)좌표평면 위에 세 점 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=197 align=absMiddle height=24><PARAM NAME="_cx" VALUE="5212"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/46.8`5.6/12,[1]{{P}_{1}(3, 4), {Q}_{2}(-6,2), {R}_{1}(3,6)}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>이 있다. 세 선분 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=128 align=absMiddle height=43><PARAM NAME="_cx" VALUE="3386"><PARAM NAME="_cy" VALUE="1137"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/30.1`8.9/12,[1]{bar{{Q}_{1}{P}_{1}}, `bar{{R}_{1}{P}_{1}}, `bar{{P}_{1}{Q}_{1}}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 의 중점을 각각 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=79 align=absMiddle height=24><PARAM NAME="_cx" VALUE="2090"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/18.6`5.6/12,[1]{{P}_{2}, {Q}_{2}, {R}_{2}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 라 하고, 세 선분 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=128 align=absMiddle height=43><PARAM NAME="_cx" VALUE="3386"><PARAM NAME="_cy" VALUE="1137"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/30.1`8.9/12,[1]{bar{{Q}_{2}{P}_{2}}, `bar{{R}_{2}{P}_{2}}, `bar{{P}_{2}{Q}_{2}}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>  <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=30 align=absMiddle height=30><PARAM NAME="_cx" VALUE="793"><PARAM NAME="_cy" VALUE="793"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/3.1`4.3/12,[1]{}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 중점을 각각 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=79 align=absMiddle height=24><PARAM NAME="_cx" VALUE="2090"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/18.6`5.6/12,[1]{{P}_{3}, {Q}_{3}, {R}_{3}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이라 하자. 같은 방법으로 얻어지는 점 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=215 align=absMiddle height=24><PARAM NAME="_cx" VALUE="5688"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="4063280"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/50.1`5.6/12,[1]{{P}_{n}, {Q}_{n}, {R}_{n} (n`equal` 1, 2, 3, `hdot3` )}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 에 대하여 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=19 align=absMiddle height=24><PARAM NAME="_cx" VALUE="502"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/4.5`5.6/12,[1]{{P}_{n}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 의 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=30 align=absMiddle height=30><PARAM NAME="_cx" VALUE="793"><PARAM NAME="_cy" VALUE="793"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/3.1`4.3/12,[1]{}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=12 align=absMiddle height=18><PARAM NAME="_cx" VALUE="317"><PARAM NAME="_cy" VALUE="476"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/2.8`4.3/12,[1]{y}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 좌표를 <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=18 align=absMiddle height=24><PARAM NAME="_cx" VALUE="476"><PARAM NAME="_cy" VALUE="635"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/4.3`5.6/12,[1]{{a}_{n}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT> 이라 할 때, <OBJECT class=MATH classid=clsid:70E4BF88-2729-4A46-8794-D459BAC0EB63 width=46 align=absMiddle height=41><PARAM NAME="_cx" VALUE="1217"><PARAM NAME="_cy" VALUE="1084"><PARAM NAME="BackColor" VALUE="3932222"><PARAM NAME="Enabled" VALUE="-1"><PARAM NAME="Script" VALUE="[0]#wh4/11.3`9.8/12,[1]{6`sum_{n`equal`1}^{inf}`{a}_{n}}/{#xc333333}"><PARAM NAME="FontSize" VALUE="12"><PARAM NAME="FontColor" VALUE="3355443"><PARAM NAME="Editable" VALUE="0"><PARAM NAME="Measurable" VALUE="0"></OBJECT>의 값을 구하시오. (풀이는 첨부파일에...)

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