٥륯åĥ

520̤
712̤
91̤
ƻˤ٤ƿ41̤ꡣ
1215ڡ 0:07:20 52040
ɥȥ
32ξ
3Ĥ1̤ꡢ1Ľ2Ĥ2̤η3̤ꡣ
34ξ
2ܤǶڤΤ33=9̤ꡢ
ǤʤΤ2̤η11̤ꡣ
36ξ
2ܤǶڤΤ311=33̤ꡢ
ǤʤΤ42=8̤η41̤ꡣ
1ٷиʤΤǤ׻˼ꤳäƤޤޤ
1215ڡ 0:12:03 52041
Mr.ǥ
ΤʬǤ
2ܤξ....33327̤
1ܤξ硡32212̤
0ܤξ......2̤
ɡ27+12+241̤
Ȥޤ
ڻԡ 1215ڡ 0:19:22 52042
鯤ο
2n3ξοAnȤơA3롣

A1ˤĤ
23ξ֤ϡ3̤ʤΤǡ
A13

A2ˤĤ
A1ȱA1ˤޤ륿뤬ʤ礬A1*A19̤ꡣ
A1ȱA1ˤޤ륿뤬礬2̤ꡣ
A29+211̤ꡣ

A3ˤĤ
(a)A2ȱA1ˤޤ륿뤬ʤ礬A2*A133̤ꡣ
(b)A1ȱA2ˤޤ륿뤬ʤ礬A2*A133̤ꡣ
(c)2ϡA1A1ȱA1ˤˤޤ륿뤬ʤA1*A1*A1=27̤ꡣ
(d)A1A1ˤޤ륿뤬ꡢA1ȱA1ˤˤޤ륿뤬礬2̤ꡣ
A4=33+33-27+241̤ꡣ

//
1215ڡ 0:37:06 52043
⡼ޥ
ǥǤΤ...
0ܤξ...
-- -- --
| -- -- |
| -- -- |
ȡŷϵդ2ĤȴƤޤ...^^;
1215ڡ 0:37:14 52044
Ȥ
#49328
#49329

ΤηǼĤDzԤDz򤤤Ƥơ
äͭMthematicaäǤ
̵Maximaǡ

product(product((4*cos(j*%pi/4)^2+4*cos(k*%pi/7)^2)^(1/4),j,1,3),k,1,6)$
float(%);

41()
˭ԡ 1215ڡ 1:31:45 MAIL:fttnm528@ybb.ne.jp 52045
Ȥ
#52045

ʥ쥹Ǻm*n=3*6Ǥ

ev(product(product((4*cos(j*%pi/(m+1))^2+4*cos(k*%pi/(n+1))^2)^(1/4),j,1,m),k,1,n),m=3,n=6)$float(%);

Τ褦ˤƿͤѤƤǤǸͭѤǤ͡ä!!
˭ԡ 1215ڡ 1:45:23 MAIL:fttnm528@ybb.ne.jp 52046
ֿء׾ι
ʣɤ뤫Ǥ
ɡ˲֤Ĥ֤ʬơüͤƤޤ
1215ڡ 9:38:52 52047
ǯ
4Ǿʬơ夲
___1Ĥ2塦塦Ȥ___
(1111)(1112,1121,1211,2111)(1122,2211)(1221,2112)4Ȥʤ
2,3,4ܤϡ⤦Ĥΰ֤Ǿʬ̤
3*1+(1+3)*4+(2+4)*2+(3+2)*2=41
1215ڡ 17:50:45 52048
ߤ
ʤˣߣĹģ̤
ʤˣߣĹʽĤʬǤǤʤˡģ̤
ʤˣߣĹʽĤʬǤǤʤˡģ̤

ƣ߲Ĺ
ܤܤߣߣᣲ̤
ܤߣ᣶̤
ܤߣ᣶̤
̤
Ĥʬ䤬Τǡܣܣܣᣴ̤ꡣ

ƻ˾ʬǤǤΤǡȤƤɸŪꡣ
ȤǤꤵ줿ȤΤǤϡ
1215ڡ 20:02:27 52049

Mr.ǥ#52042 ȤۤƱͤ˲򤭤ޤ̲ͤޤ

3, 2n ĹߤĤοA(n)̤Ȥ
A(1)=3
A(2)=3^2+2=11

A(3)ϡA(2)κޤϱ2Ѥ­硢(222)ʣΤǤξο2Ǥⱦ2Ǥڤʤ(6)ξο­Ф褤Τǡ
A(3)=A(2)A(1)2-{A(1)}^3+2
=66-27+2=41̤

ƱͤA(4)ϡA(3)κޤϱ2Ѥ­ƽʣ(2Ƥ42)ξοӱ2Ƕڤʤ(8)(44)ξο­Τǡ
A(4)=A(3)A(1)2-{A(1)}^2{A(2)}+2+2^2
=246-99+2+4=153

A(5)ϡʣ(2Ƥ62)ǡӱ2ǶڤʤΤ(10)(4ã)(64)(424)ʤΤǡ
A(5)=A(4)A(1)2-{A(1)}^2{A(6)}+2+2^2+2^2+2A(1)2
=918-369+2+4+4+12=571

Ʊͤ˹ͤơA(6)=2131ġ
ޤǸĤǤꤴŦ
̲ʣ᤮˴ǰޤ

1215ڡ 20:43:47 52050

#52050

ޤ
A(5)=A(4)A(1)2-{A(1)}^2{A(6)}+2+2^2+2^2+2A(1)2
=918-369+2+4+4+12=571



A(5)=A(4)A(1)2-{A(1)}^2{A(3)}+2+2^2+2^2+2A(1)2
=918-369+2+4+4+12=571
1215ڡ 21:30:07 52051
ޡޤ
󡩤ɤäؼλǸФ޶
Х󥹤ʤäʤ 1215ڡ 21:35:19 HomePage:ĥåǿäƤ52052
ֿء׾ι
#52050̲ˤĤơͤƤߤޤ
A(0)=1Ȥޤ
A(1)=A(0)+2A(0)
A(2)=A(1)+2{A(0)+A(1)}
A(3)=A(2)+2{A(0)+A(1)+A(2)}
A(4)=A(3)+2{A(0)+A(1)+A(2)+A(3)} Τ褦ˤʤäơ
A(n+1)=A(n)+2(k,0,n){A(k)}ʤꤿĤ褦ʡ
1216ʶ 7:55:47 52053
ֿء׾ι
#52053
ȤȤǡA(n+2)-4*A(n+1)+A(n)=0,A(0)=1,A(1)=3Ω
򤯤ȡA(n)=(2+3)^(n-1)*(5+33)+(2-3)^(n-1)*(-5+33)Ȥʤޤ
1216ʶ 8:47:38 52054
Ϸ
դǤΤ褦˲򤭤ޤ
硢ģ硡ߣã
硢ģ硡ߣã
硢ģ硡ߣã
硢ģ硡ߣã
ס̤
1216ʶ 9:02:50 MAIL:takaaki-k@aqr.bbiq.jp 52055
ߥȤ
򤹤ä˺ƤޤäƤޤϷͤΤ褦˾ʬ򤷤ƤȤޤ
Ϸϡ 1216ʶ 9:18:13 52056

#52053#52054
ֿء׾ιԤ

򤤵§򸫤ĤƤޤƤ꤬Ȥޤ
Ϥ狼ꤽǤ狼ʤǤ
򤤤ƤߤΤǤ
A(n)=1/6{(3+3)(2+3)^n+(3-3)(2-3)^n}
ˤʤ褦ʵޤְäƤ餴ƼϤޤ
1216ʶ 11:15:18 52057

#52054١פޤ
ֿء׾ιԤޤβϱΤ23dzΩ褦˻פޤ
1216ʶ 11:32:42 52058
ֿء׾ι
#52057,#52058ʥޥ
ڤ򤢤꤬Ȥޤä̤ǤȴƤޤwww
§ΤȤˤĤơʬˤ⤷ޤ󤬡ʲ̤Ǥ

֤Ĺ򡡡

֤Ĺ򡡡ɽȤˤޤ

A(n)ξοޤǺü֤ƤȤˤޤ礦
ááá
áááááá
ááá
3̤A(1)ο޷ǡα¦A(n-1)ο޷ˤʤޤΤǡA(1)A(n-1)̤Ǥޤ
2̤ˤĤƤϡ1ܤϡ³

ááʤ顢α¦A(n-2)ο޷ˡ
á


áʤ顢2Ĥäʤ顢α¦A(n-3)ο޷ˡ
á
ʤ顢ޤǤη֤ˤʤäƹԤޤ
ǸαüǤϡ
ááǡüηǷޤäƤɤ餫ˤʤޤ
á

ĹĤʬƿƤΤǤε§˵դޤ
1216ʶ 12:32:34 52059

#52059
ֿء׾ιԤ
ȤƤ狼פäǤ
򤷤ޤ
꤬Ȥޤ
1216ʶ 14:05:54 52060
ߤ뤯
A(n+1)=A(n)+2(k,0,n){A(k)}

A(n+2)-4*A(n+1)+A(n)=0
äƤɤΤ褦ʼѷƳƤޤ
1216ʶ 19:13:59 52061

#52061ߤ뤯

Ǥߤޤ󡢡
nn-1زĤꡢ2Ĥμΰ򤷤ޤ
A(n+1)=A(n)+2(k,0,n){A(k)}
A(n)=A(n-1)+2(k,0,n-1){A(k)}
μ鲼μ
A(n+1)-A(n)=A(n)-A(n-1)+2A(n)
ȤʤޤΤǤȤϰܹnn+1ؾ夲еޤޤ
1216ʶ 20:49:42 52062
ߤ뤯
#52062
꤬Ȥޤ
1216ʶ 22:15:39 52063
äѥȥ
Υ֥åĤʬĤΥ֥å
A:Ĺ3
B:夬ĹĹ
C:夬Ĺ2硢Ĺ
Ȥ롣
BƱΡCƱΤܤϡܤĹĹ֤뤳ȤǤ롣
֥åĤξA,B,Cƣ̤ꡣ
֥åĤξʹߤϺǸΥ֥å¤ʬषưʲɽΤ褦ˤʤ롣
ǸAľ¤A,B,C٤OK
ǸBľ¤A,B,C٤ƹԤ뤦ˡBBȾ嵭֤ǽʤᡢľBξοϣܤ˥Ȥ롣

Aܣܣᣳܣܣᣱ
Bܣߣܣᣴܣߣܣᣱ
Cܣܣߣᣴܣܣߣᣱ
äơܣܣᣴ(̤)
1216ʶ 22:35:49 52064