ޥ
¤ϤޤҤäꤷ...orz

ϩˤĤޤ˥ߥȤĤޤ衼ˡ(^^;;
PowerBook G4 119ڡ 0:06:51 MAIL:masaru-y@sansu.org HomePage:26502
ȥȥ
Ϣ³ǣ˵ǺīϣȾǤ
Ǥ⡢ʤƤΤDz򤤤Ƥߤޤ׻ߥ򤷤Ƥޤ
䤹ߤʤ
ʼ˸лԡ 119ڡ 0:13:35 MAIL:h-sakai@zb3.so-net.ne.jp 26503
ڼ
͵ʤǤ
Ϣ³̤ƨƤޤޤʾǤ
ϤƤ
ȣΤ򤤤ȡ
͡ 119ڡ 0:19:00 MAIL:iida@ae.keio.ac.jp 26504
ڼ
͵ʤǤ
Ϣ³̤ƨƤޤޤʾǤ
ϤƤ
ȣΤ򤤤ȡ
͡ 119ڡ 0:21:00 MAIL:iida@ae.keio.ac.jp 26505
ڼ
͵ʤǤ
Ϣ³̤ƨƤޤޤʾǤ
ϤƤ
ȣΤ򤤤ȡ
͡ 119ڡ 0:23:12 MAIL:iida@ae.keio.ac.jp 26506
CRYING DOLPHIN
Ρȿ̲ͣʬѤץС
ȤޤʤƤä
ǯԥ奦ȡ 119ڡ 0:24:54 HomePage:ȤƻȤ26507

轵ΤϤäꤳ˺Ƥ
ƺǯ黻ϤäϢ³ޤϹäƤƤˤɤ失ʤɤ

ߴֽ˶ƤΤӤãʤƤޤʤäƴ򤷤ΤǤ͡
119ڡ 0:27:25 26508
tomh
#26506

nΤȤѤϡ9(4n+1)/[4n(2n+1)^2] cm^2 ?

ԡ 119ڡ 0:39:28 MAIL:tomh@yahoo.co.jp HomePage:H to M26509
mhayashi
(1.5+1)*1/2=1.25
ǤǤ͡
ִC-DȤΡʲ򤱤ʤäפФޤ
ä򤱤뤫ʤ
119ڡ 1:04:15 HomePage:M.Hayashi's Web Site26510
CRYING DOLPHIN
껶餫λij
http://www7a.biglobe.ne.jp/~cdcdcd/pikkachu-125.GIF

䤢βޤäƤʤ䡣
ϣ٤ۤɺäȤɤɤ⹹
Уúƥ󥹥ȡ뤹Ϥ˴٤äơϫƺä
äƺƺ뵤Ϥ򼺤äƤΤ
ǯԥ奦ȡ 119ڡ 1:26:00 HomePage:ȤƻȤ26511
kasama
Ϥ褦ޤʴǤޤ(^_^;
http://wind.ap.teacup.com/kasama/img/1137634503.jpg
119ڡ 10:38:02 26512
uchinyan
(ɲýޤ)
Ϥˤϡϡ빽ͤޤ
褯褦ˡϰϤζõޤ̥Ǥθ֤ P Ȥޤ
ޤP AB ˤȤϡAB, BC, CD ȿ͡ޤ֤ơAD ˹Ԥ褦ˤ뤿ˤϡ
ŸޤΤǹͤȡ2cm < AP < 3cm ϰϤʬޤϤʬޤ
BF ǡǽ顢ABCD EFGH ˤȴ㤤ơۤʤȤ򤤤ȹͤƤޤޤ (^^;
(ȤϤΤΡϡޤطʤǤ͡)
ְ㤤ˤäȵդƹ͡塢äʸȤޤ
AB AX = x cm Ȥơ̥ X BF ʿԤ EF Ȥθ Y Ȥޤ
ۤɤξϡ2 < x < 3 ˤʤޤ
P XY ˤȤȿ̥ͤã褦äƤȤBF Ѳ򡢻ѷȤäĴ٤ȡ
P AB 鲼 x/2 cm ޤǤˤФȤʤޤۤɤξꡢ2 < x < 3 äΤǡ1 < x/2 < 3/2 Ǥ
ȤˡX AB ưȡɡP ϡ
BS = 1 cm Ȥʤ AB S
BT = 3/2 cm Ȥʤ BF T
S BF ʿԤ̥ SU = 1 cm Ȥʤ U
B
λͤĤʤˤФȤʬޤǡѤϡ
1/2 * (1 + 3/2) * 1 = 5/4 cm^2
ˤʤޤ
ͥνȡ 119ڡ 13:28:32 MAIL:uchi@sco.bekkoame.ne.jp 26513
2709
ޤȤäƤޤ1Τڡǡ
ѥˤޤäƤ롡 119ڡ 14:37:12 26514
2709
Ǥ
ѥˤޤäƤ롡 119ڡ 14:37:51 26515

̣ģȣṬ̌ãģȣạ̇̄£ãǣợ£ƣŤνоݰươĤģġĤ¤٤褦ʷ񤤤Ƶޤ
119ڡ 15:13:48 26516

󤵤βǤΡޥǤ褦ʵޤ⤵ξȲˤȤǡ̤ΡüüͤȤ椬飱ѲƤȤܤФ褤ΤǤ͡
119ڡ 17:25:04 26517
uchinyan
⤤˻äȡǼĤɤߤޤ
#26511, #26516, #26517
ΤˤǤ ^^;
#26513Ÿ޵ڤϡƱȤˤʤ褦ʵ⤷ޤޥǤ͡
#26512
ࡢޤϤ줤ʤɡʤ褯ʬʤ (^^;
#26509
#26513˴ŤƤäƤƱˤʤޤ
׻ص塢ΩΤΰդ 1cm ȤޤȡƱͤ AX = x cm Ȥơ
AB, BC, CD, DA Фơ1 ܤθϡ
AB ֡x, 1 - x, BC ֡1/x - 1, 2 - 1/x, CD ֡2x - 1, 2 - 2x, DA ֡2/x - 2, 3 - 2/x
ȳդʬƤޤǡ1 ܤ̥˼ޤˤϡꥮꡢ
2/x - 2 = 1, x = 2/3
ǡǽ̥˼ޤˤ 0 < x < 1 顢ɡ2/3 < x < 1 Ǥ
BF ϡǽ̥Ȥ y Ȥȡ̥ǡꥮꡢ
y + y * (1/x - 1) + y * (2 - 1/x) + y * (2/x - 2) = (y + y) + y * (2/x - 2) = y * 2/x = 1
ˤʤФ褯y = x/2 ǡ1/3 < y < 1/2 Ǥ줫顢1 ܤξ#26513ϰϤʬꡢѤϡ
S/9 = 1/2 * (1/3 + 1/2) * 1/3 = 1/9 * 5/4
ºݤˤϡΩΤΰդ 3cm ʤΤǡ3 * 3 = 9 ܤ 5/4 cm^2 Ǥ
ƱȤ n ˳ĥưפ˷׻ǤơǸ DA ֤ϡ2n/x - 2n, (2n+1) - 2n/x ˤʤޤ
ǡƱͤ˥ꥮͤơ
2n/x - 2n = 1, x = 2n/(2n+1), 2n/(2n+1) < x < 1
(y + y) + ...n... + (y + y) + y * (2n/x - 2n) = 1, y = x/2n, 1/(2n+1) < y < 1/2n
ˤʤꡢѤ
S/9 = 1/2 * (1/(2n+1) + 1/2n) * 1/(2n+1) = (4n+1)/(4n(2n+1)^2)
S = 9(4n+1)/(4n(2n+1)^2) cm^2
ˤʤޤ
ͥνȡ 120ʶ 11:45:11 MAIL:uchi@sco.bekkoame.ne.jp 26518
kasama
#26518 uchinyan

ߤޤǤ<(_ _)> ѿޤ狼񤤤Ǥ͡_)
ʬǡпɤȿͤƤϩŬˤĤʤΤɽäΤǤ

http://wind.ap.teacup.com/kasama/img/1137682130.jpg
119ڡ 23:53:13 26519
uchinyan
#26519kasama ءοޤ򤢤꤬Ȥޤ
ʤۤɡȤǤ
ޤƤޤΤϤǤ͡
ϡŸ褦ʡޤ֤ޤ񤤤ꡢü򲡤ꤷơȤʬޤ
ͥνȡ 120ʶ 8:55:36 MAIL:uchi@sco.bekkoame.ne.jp 26520
tomh
#26518
> #26513˴ŤƤäƤƱˤʤޤ

Ǥ¿ޤ (^.^)

uchinyan󡢤Ĥ餷򤢤꤬Ȥޤ (^o^)
ԡ 121ڡ 0:38:25 MAIL:tomh@yahoo.co.jp HomePage:H to M26521
⡼ޥ
ä줿
Ƭ󤬤ޤ
Ϥ1/3ʬäΤǤʤʤ
ȤƤϡ9*1/3*(1-1/3-1/4)=5/4 ǤΤʡ

ɤ⡢ǼĤߤ¤錄ˡϴְ㤤ʡޤäߤǤ͡錄ΤǤʤʡ
121ڡ 9:02:37 MAIL:kennji72001@yahoo.co.jp 26522
uchinyan
tomh
uchinyan󡢤Ĥ餷򤢤꤬Ȥޤ (^o^)
βˡ˴ؤƤϡϤꡢΩΤоΤ˰ưϻ¤٤롢#26511, #26516, #26517ʤɤñǤ͡
̲⡢ǤΤ⤷ޤ
(äɲ)
#26516 ήˤȡ
2n(2n+1)Ĥ (2n+1)ġ2nĤ¤٤褦ʷ
ͤФǤ͡ʤ⤵ϡ1ʬǤ
(ɲäޤ)

ϡνǤ
ؼϡ󥿡Ǥ͡֤ȤפʤĴ˴ĥäߤΤǤ
ͥνȡ 121ڡ 11:41:15 MAIL:uchi@sco.bekkoame.ne.jp 26523
⡼ޥ
ΤƤ򤤤ɶʤʿޤ򸫤ƤĤƤʤǤͤ
Ǥ⡢ƤߤˤʤꤽʤΤŪʬäƤޤ

طʤǤʲͤƤޤʥմ֤ȿͤοȤ̣ǤϤäȤϴϢ뤫


anѤ򼡤Τ褦롣
a1=1n1ΤȤa(n+1)=an+1/an
ΤȤa100ʬ[a100]衣

122 17:36:07 MAIL:kennji72001@yahoo.co.jp 26524
weapon
14
122 21:15:56 26525
⡼ޥ
#26525
weaponءä򤫤ޤ
ɤäƲ򤫤줿ΤǤ礦
褫ä鶵Ʋޤ

ʤߤͧͤβϤޤǤ錄ϡ

(a_(n+1))^2=(a_n+1/(a_n))^2=(a_n)^2+(1/a_n)^2+2 顢

(a_2)^2-(a_1)^2=(1/a_1)^2+2
(a_3)^2-(a_2)^2=(1/a_2)^2+2



(a_100)^2-(a_99)^2=(1/a_99)^2+2

(a_100)^2-(a_1)^2=(1/a_1)^2++(1/a_99)^2+2*99
(a_100)^2=(1/a_1)^2++(1/a_99)^2+199
=200+(1/a_2)^2++(1/a_99)^2

a_2=2
(1/a_2)^2=1/4

200=102=14.
15^2=225

Ĥޤꡢ1/4*98=98/4<100/4=25 ʤΤǡ
200<(a_100)^2<225
Ĥޤꡢ14<a_100<15
Ĥޤꡢa_100 ʬϡ14

äƴǷ빽ƻ˹ͤޤ
ȾϤޤ޻פĤΤǤ
ˡʤ͡
122 21:39:05 MAIL:kennji72001@yahoo.co.jp 26526
weapon
ƱǤ
䴰ȡ

2nΤȤa_n=a_(n-1)+{1/(a_(n-1))}2()(1/(a_n))^21/4

123ʷ 0:05:12 26527
⡼ޥ
#26527
weapon󡢤꤬Ȥޤ
̤ˤ⡢a_n ʬϡ2n ʬˤʤꤽǤ͡
123ʷ 0:11:56 MAIL:kennji72001@yahoo.co.jp 26528
uchinyan
#26524 ¾
äȸʤ֤ˡ⡼ޥ󤵤夬äơ᤯⡢«Ƥޤޤ͡
#26526DzˡϿԤƤȻפΤǡΰ̣ǤϥȤϤʤΤǤ
褹뤳Ȥ˵դʤǤ⤦ޤʤΤʤȻפäơ򾯤ͤƤߤޤ
ˡȤƤϡʥ֤ȻפΤǤʬɾԽʬʤΤǡǰʤ鼺ԺǤ
̤Ϥäȶ̣ΤǡͤޤǤˡ𤷤Ƥޤ

ޤ餫ˡa(n) ñĴäǤǡ a(n) ʬ k >= 2 Ȥȡ
ǽʬ k ˤʤΤޤ a(n) Ȥޤ
ΤȤa(n-1) < k ǡ
a(n) - (k + 1/k) = a(n-1) + 1/a(n-1) - k - 1/k = (a(n-1) - k) * (1 - 1/(a(n-1) * k)) < 0
Ĥޤꡢa(n) ξʬ b(n) 1/k ⾮ʤޤ
a(n) Фơ
a(n+m) = a(n) + 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1)
Ǥa(n+m-1) ޤǤʬ k Ȥȡ
1/(k+1) < 1/a(n+m-1) < ... < 1/a(n+1) < 1/a(n) <= 1/k
m/(k+1) < 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1) < m/k
ǡa(n) ξʬ b(n) ͤ
m/(k+1) <= b(n) + m/(k+1) < b(n) + 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1) < b(n) + m/k < 1/k + m/k
ơa(n+m) ʬ k+1 ˤʤˤϡ
Ǹꡢm <= k-1 Ǥ a(n+m) k ʳʬ 1 꾮ʤΤǡm >= k ɬפǤ
ޤǽꡢm >= k+1 a(n+m) k ʳʬ 1 ʾʤΤǡ
m = k+1 a(n+m) ʬ k+1 ˤʤСm >= k+2 ǤΩޤ
äơ̤ˡa(n) ʬ k a(n+m) ʬǽ k+1 ˤʤϰϤ m k <= m <= k+1 ˤʤޤ
Ĥޤꡢϡʬ k ˤʤ褦 a(n) θĿϡk k+1 ȤȤǤ
ξ󤫤顢ʬ k ˤʤ褦 a(n) θĿ٤ k ξΡ
ʬ k ޤǤ a θĿϡk(k+1)/2 Ǥ
a(100) ͤƤΤǡk(k+1)/2 >= 100 Ĥޤ k >= 14 Ǿޤ
ϡa(100) ʬ 14 ˤʤ뤳Ȥ̣ޤ
ǰʤ顢ʬ k ˤʤ褦 a(n) θĿ٤ k+1 ξͤ졢
ξϡk = 1 1 ĤǤ뤳Ȥθ (k+1)(k+2)/2 - 2 >= 100 ǡk >= 13 Ȥʤޤ
ºݤˤϡʬ k ˤʤ褦 a(n) θĿ k ä k+1 äꤹΤǡ
k ϡ13 14 ǤϷǤʤ褦Ǥ
ΨŪˤɤˤʤ뤫ȾȲꤹȡ k(k+1)/2 + k/2 = k(k+2)/2 Ȥʤꡢ
k = 14 Ȥʤäơa(100) ʬ 14 ʤͽۤǤޤ
ץȤ a(1000000) ޤǥåƤߤޤ
ֳΨŪˤɤˤʤ뤫ȾפȤΤϡ褽ʴǤΤ 1/2 ǤϤʤ褦Ǥ
a(100) ʬ 14 ȤΤåǤޤ
⤦ɾ򤦤ޤСΥʥ֤ˡǤ⡢ˤɤ失뤫⤷ޤ (^^;

(äɲ)
a(n)#26526ˡǤΤޤɾ
(1) sqrt(2n) < a(n) < sqrt(2n + (n-2)/4) = sqrt(9n-2)/2
ˤʤ褦ǤֳΨŪˤɤˤʤ뤫Ⱦפβ줿嵭ˡǤϡ
(2) k >= sqrt(2n+1) - 1 Ǿ k
ˤʤޤn = 20000 Ȥȡ
(1) 200 < a(20000) < 212.13...
(2) k >= 199.0024..., k = 200
ץˤ׻Ǥϡ[a(20000)] = 200 Ȥʤޤ
⡼ޥ󤵤ͽۡ[a(n)] = [sqrt(2n)] Ǥ(1)ɾϡΤޤޤǤϾŤ褦Ǥ
Ǥ(1/a(2))^2 + (1/a(3))^2 + ... + (1/a(n-1))^2 ɾθľɬפˤʤޤ͡
ͥνȡ 123ʷ 22:56:40 MAIL:uchi@sco.bekkoame.ne.jp 26529
⡼ޥ
#26529
uchinyanء
ܤϤɤǤ
>a(n+m) = a(n) + 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1)
˥ԥȤʤäꤹΤǤ
ʤ⤦ʬ䤹Ƥޤ

n ΰ̤ξ礬ɤʤ뤫ͤƤߤǤ
(a_n)^2=2*(n-1)+2+(1/a_2)^2++(1/a_(n-1))^2
=2n+(1/a_2)^2++(1/a_(n-1))^2
<2n+(n-2)/4
2nm^2
(m+1)^2=m^2+2m+1
2n+(n-2)/4m^2+(m^2/2-2)/4
Ĥޤꡢ2m+1 (m^2/2-2)/4 礭ͤƤߤȡ
m^2-4-8(2m+1)=m^2-16m-12=(m-8)^2-76 ʤΤǡ
m-89 ʤ顢Ĥޤꡢm17 Ĥޤꡢm 17ʾʤ顢a_n ʬ m+1 ʾ塣
m-88 ʤ顢Ĥޤꡢm16Ĥޤꡢm 16ʲʤ顢a_n ʬm
Ȥȡ
顢2n16^2=256,Ĥޤꡢn128 ޤǤ a_n ʬϡ2n ʬ m
2n17^2=145.5,Ĥޤꡢn146 ξϡa_n ʬϡ2n ʬ m +1 m+1 Ȥʤꤽ
δ֤οϤɤʤʤ󤫤Ǥ
123ʷ 22:43:17 26530
uchinyan
#26530
>a(n+m) = a(n) + 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1)
䤳˥ԥȤʤäꤹΤǤ
ñˡͿ줿Ȥäơ
a(n) + 1/a(n) + 1/a(n+1) + ... + 1/a(n+m-1)
= a(n+1) + 1/a(n+1) + 1/a(n+2) + ... + 1/a(n+m-1)
= a(n+2) + 1/a(n+2) + ... + 1/a(n+m-1)
= ...
= a(n+m-1) + 1/a(n+m-1)
= a(n+m)
ȤѷǤ
̤ξǤ#26529ɲʬ
n 礭ʤȡ⡼ޥ󤵤ˡϡΤޤޤǤɾŤʤޤ
ǡa(n) 礭ʤäƤΤǡ¤̵ȯ롢(1/a(n))^2 <= 1/4 ǤԽʬȻפޤ
餫鸫ľɬפꤽǤ
ʤˡȡ[a(n)] = k Ȥʤ a(n) θĿ k k+1 Ȥ郎ƳƤΤǡ
n 礭ʤäƤɾٹ礤ϤޤѤʤ褦Ǥ
k k+1 ֳΨŪˤɤˤʤ뤫ȾפβΤ񤷤Ǥ
ץˤå¸ǤϡʴǤ
βΤȤǤϡ[a(n)] ϡ
(2) k >= sqrt(2n+1) - 1 Ǿ k
ˤʤޤ줬 [sqrt(2n)] ɤϤޤǤƤޤ󤬡
ºݤ˾׻ϰϤǤϰפ褦Ǥ
ͥνȡ 123ʷ 23:44:16 MAIL:uchi@sco.bekkoame.ne.jp 26531
⡼ޥ
#26531
uchinyanء
ϸƤߤгΤˡ
̤ξɾΤ˴Ťޤ͡

ɲáʤߤˡɾǤϡn=101 ˤʤäü2n=202,15^2=225,225-202=23,(101-2)/4=24.75>23
ʤΤǡ[a_101]=15 ˤʤä㤤ޤ͡
n<100 Ǥ⡢ɾǤϷʤäƤΤʡ
124ʲС 14:49:31 MAIL:kennji72001@yahoo.co.jp 26532
uchinyan
#26532
n<100 Ǥ⡢ɾǤϷʤäƤΤʡ
ˤʤäƾĴ٤Ƥߤޤפˡ
sqrt(2n) sqrt(2n + (n-2)/4) = sqrt(9n-2)/2 Ȥͤ٤褦ʤΤʤ
櫓Ǥ顢ʤꤿ󤢤褦Ǥ
㤨Сn = 12, ...(ά)..., 88, 89, 90, 91, 92, 93, 94, 95, 96, 97
ࡢͤȡa(100) ȤΤϡʤŪ˺줿Τ褦ʵ⤷ޤ͡
ʤγΨ١Դˡ⡢ԴʤäơܤǰĤƤޤ褦Ǥ ^^;
Ψ١ǤϤʤĽФƷǤʤϡޤĤͿޤ
⤦ɤǤʤʡ
ͥνȡ 124ʲС 17:30:23 MAIL:uchi@sco.bekkoame.ne.jp 26533