#1
|
||||
|
||||
⨷Âì¤Ô´àÅ¢àÃçÇ
__________________
21 ¡Ã¡®Ò¤Á 2009 12:32 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm |
#2
|
||||
|
||||
¡çäÁèÃÙé¨Ðãªéä´éÃÖà»ÅèÒÍèÒ¹Ð
1. ¨§ËÒ¤èҢͧ $2552^2-2551^2+2550^2-2549^2+....+2^2-1^2$ 2. ¨§¤Ó¹Ç³¼ÅºÇ¡ $\frac{1}{2009}+\frac{2}{2009}+\frac{3}{2009}+...+\frac{2009}{2009}$ 3. ¨§·Í¹ $\frac{87878787\times 65656565}{78787878\times 56565656}$ à»ç¹àÈÉÊèǹÍÂèÒ§µèÓ 4. ¨§ËÒ¤èҢͧ $\frac{111}{1+1+1}+\frac{222}{2+2+2}+\frac{333}{3+3+3}+...+\frac{999}{9+9+9}$ 5. ¨§ËÒ¤èҢͧ $\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+....+20092552}$ 6. ¨§ËÒàÈɨҡ¡ÒÃËÒà $1234567898765432123456789876543212345678987654321$ ´éÇ 11 7. ¨§ËÒàÈɨҡ¡ÒÃËÒà $4444444.....(ÁÕ 4 ÍÂÙè 20092552 µÑÇ)$ ´éÇ 7 8. ¨§ËÒàÈɨҡ¡ÒÃËÒà $12345678910111213141516....255025512552$ ´éÇ 16 9. ¨§¤Ó¹Ç³¼Å¤Ù³ $(0^3-2210)(1^3-2209)(2^3-2208)....(2210^3-0)$ 10. ¨§¤Ó¹Ç³¼ÅºÇ¡ $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{2552\times 2553}$ 11. ¨§ËÒ¤èҢͧ $2(28^2)+29^2-16^2-15^2+9^2$ 12. ¨§ËÒÇèÒ ¼Å¤Ù³ $1\times 2\times 3\times 4\times 5\times ....\times 2009$ ŧ·éÒ´éÇ 0 ·Ñé§ÊÔ鹡ÕèµÑÇ 13. ¨§¤Ó¹Ç³¤èҢͧ $\frac{1(2)+2(3)+3(4)+....+999(1000)}{1000}$ 14. ¨§ËÒÊèǹ·Õèà»ç¹·È¹ÔÂÁ¢Í§ $\frac{1+11+111+1111+11111+....+1111...(ÁÕ 1 ÍÂÙè 2009 µÑÇ)}{100}$ 15. ¨§àŢⴴã¹ËÅѡ˹èÇ¢ͧ $2009^{2009^{2009^{2009^{.^{.^{.}}}}}}$ àÁ×èÍÁÕ 2009 ·Ñé§ÊÔé¹ 2009 µÑÇ 16. ¨§ËÒàÈɨҡ¡ÒÃËÒà $1\times 2\times 3+2\times 3\times 4+3\times 4\times 5+...+2007\times 2008\times 2009$ ´éÇ 2010 17. ¨§¤Ó¹Ç³¤èҢͧ $\frac{13^{2009}+25(13^{2006})+5(13^3)+125}{13^{2006}+5}$ 18. ÁըӹǹàµçÁºÇ¡¡Õè¨Ó¹Ç¹·Õèà»ç¹µÑÇ»ÃСͺ¢Í§ 2009200920092009 19. ¨§ËÒËÃÁ.¢Í§ 123123123123 , 456456456456 áÅÐ 789789789789 20. ¶éÒàÃÒàÃÕ¹ 2553 ã¹ÃÙ»¢Í§ $2^a+2^b+2^c+2^d+...$ àÁ×èÍ a,b,c,d,.... à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ËÃ×Í 0 «Öè§áµ¡µèÒ§¡Ñ¹ áÅéÇ a+b+c+d+... ÁÕ¤èÒà·èÒã´ 11 ¡Ã¡®Ò¤Á 2009 07:01 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 8 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Scylla_Shadow à˵ؼÅ: á¡é⨷Âì |
#3
|
||||
|
||||
¢éÍ1.
$$(2552-2551)(2552+2551)+(2550-2549)(2550+2549)+...+(3-2)(3+2)+(2-1)(2+1)$$ $$2552+2551+2550+...+3+2+1=(2553)(\frac{2552}{2})=3257628 $$
__________________
||!<<<<iNesZaii>>>>!||
10 ¡Ã¡®Ò¤Á 2009 21:50 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Ne[S]zA |
#4
|
||||
|
||||
¢Íº¤Ø³¾Õèscylla
$\frac{1}{2009}+\frac{2}{2009}+\frac{3}{2009}+...+\frac{2009}{2009}$ $\frac{1+2+3+4+5+...+2009}{2009}$ $\frac{2009*1005}{2009}$ $1005$ $µÍº 1005$ ______________________________________ ¢ÍÅÑ´¹Ð $1\times 2\times 3\times 4\times 5\times ....\times 2009$ 2009/5=401 401/5=80 80/5=16 16/5=3 $ÁÕ0=401+80+16+3=500µÑÇ$ _______________________________________ $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{2552\times 2553}$ ¾Ô¨ÒóÒ$\frac{1}{1\times 2}=1/2$ $\frac{1}{1\times 2}+\frac{1}{2\times 3}=2/3$ $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}=3/4$ ´Ñ§¹Ñé¹$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{2552\times 2553}= 2552/2553$
__________________
21 ¡Ã¡®Ò¤Á 2009 11:31 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm |
#5
|
||||
|
||||
¾ÕèʧÊÑ¢éÍ 12. ¹Ð ¾ÕèÇèÒ¹éͧËÒÃàÅ¢¼Ô´ÍèÐ
14 ¡Ã¡®Ò¤Á 2009 11:00 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Scylla_Shadow |
#6
|
||||
|
||||
¢éÍ4.
$$\frac{111}{3}+\frac{222}{2(3)}+\frac{333}{3(3)}+\frac{444}{4(3)}+...+\frac{999}{9(3)}$$ $$=\overbrace{\frac{111}{3}+\frac{111}{3}+...+\frac{111}{3}}^{9} $$ $$=9(\frac{111}{3})=333$$
__________________
||!<<<<iNesZaii>>>>!||
|
#7
|
||||
|
||||
¾Õè¤ÃѺ ¢ÍàÇÅÒ 1Çѹ¤ÃѺ à´ÕëÂǾÃØ觹ÕéÁҵͺ
__________________
11 ¡Ã¡®Ò¤Á 2009 22:11 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm à˵ؼÅ: ËÂÔ¹ËÂÒ§´Ù´Ç§ àÅÂàà¡éà¤Ãç´¤ÃѺ:haha: |
#8
|
||||
|
||||
ã¤Ãª×èÍ "¤ÃÑÂ" ¤ÃѺ ¾Õè¤ÃÑ ¨Ðä´é͹ØÒµ¶Ù¡ÇèÒ¨ÐãËéàÇÅÒ 1 ÇѹËÃ×Íà»ÅèÒ
»Å. Çѹ¹Õé¡ÃзÙéÍ×è¹ÁÕáµèà¤ÃÕ´æ à»ç¹¾Ç¡ á¡Ð ¡Ñºá¾Ð (GAT-PAT) àÅÂáÇÐà¢ÒÁҵͺ¡ÃзÙé·ÕèäÁèà¤ÃÕ´´Õ¡ÇèÒ (äÁèÇèҡѹ¹Ð¤ÃѺ) |
#9
|
||||
|
||||
ÍéÒ§ÍÔ§:
áµè·ÇèÒ â¨·Âì¾Ç¡¹Õé ÀÒÉÒÍѧ¡ÄÉÇèÒäÃËÃͤÃѺ
__________________
|
#10
|
||||
|
||||
ËÁÒ¶֧ GAT-PAT ËÃ×Íà»ÅèÒ ¶éÒãªè ¡çàªÔÈÖ¡ÉÒä´é¨Ò¡·Õè¹Õè¤ÃѺ
http://www.niets.or.th/ |
#11
|
||||
|
||||
ÍéÒ§ÍÔ§:
__________________
|
#12
|
|||
|
|||
¤Ô´àÅ¢àÃçÇ = think number quick Quick Arithmetic Quick Calculation
__________________
ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#13
|
||||
|
||||
ÍéÒ§ÍÔ§:
¤Ô´àÅ¢àÃçÇ = kid-lek-raew ¤Ó¹ÕéÁÕ·ÕèÁҹФÃѺ ¤é¹¨Ò¡ karaoke dictionary (thai-karaoke) |
#14
|
||||
|
||||
áÁè¹éÒÁÙÅ=MOTHER WATER MOON
check ãËé´éǤÃѺ 3.$145/112$ 5.$\frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+....+\frac{1}{1+2+3+....+20092552}$ $\frac{2}{1*2}+\frac{2}{2*3}+\frac{1}{3*4}+....+\frac{2}{20092552*20092553}$ $2(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+....+\frac{1}{20092552*20092553})$ ¾Ô¨ÒóÒ$\frac{1}{1\times 2}=1/2$ $\frac{1}{1\times 2}+\frac{1}{2\times 3}=2/3$ $\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}=3/4$ ´Ñ§¹Ñé¹$\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+...+\frac{1}{20092552\times 20092553}= 20092552/20092553$ $2(20092552/20092553)$ $40185104/20092553$ 11.2009 17.$13^3+25=2222$ 19.$2^7=32*4=128$
__________________
21 ¡Ã¡®Ò¤Á 2009 11:39 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 9 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm |
#15
|
||||
|
||||
Åͧàªç¤¢éÍ 3,17,19 ´Ù¤ÃѺ
ÅͧµÍºÁÒà»ç¹µÑÇàÅ¢·ÕèäÁèµÔ´àŢ¡¡ÓÅѧ´Ù¤ÃѺ |
|
|