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ÀÛ¼ºÀÚ Uploader : ÀÏ»ó´Ù¹Ý»ç ÀÛ¼ºÀÏ Upload Date: 2022-05-14º¯°æÀÏ Update Date: 2022-05-14Á¶È¸¼ö View : 248

±×¸²°ú °°ÀÌ ±æÀÌ L ÀÎ ±ÕÁúÇÑ ¹°Ã¼¸¦ ³»¹Ð¾î ½×À» ¶§, ¹°Ã¼ÀÇ °³¼ö n ¿¡ µû¶ó ³»¹Ð ¼ö ÀÖ´Â °¢°¢ÀÇ ÃÖ´ë ±æÀÌ an ¸¦ ±¸ÇÑ´Ù.

À§¿¡¼­ ¾Æ·¡·Î n ÃþÀ̶ó ÇÏ°í, n Ãþ±îÁöÀÇ ¹«°ÔÁß½ÉÀÌ n+1 ÃþÀÇ ¿ìÃø ³¡¿¡ °É¸®´Â »óŸ¦ ±¸ÇÑ´Ù.

n=1 ¿¡¼­,

a1 = L-(1/2)L = (1/2)L = c1L

n=2 ¿¡¼­,

a2 = L-(a1+(1/2)L+(1/2)L)/2
   = L-(c1+(1/2)+(1/2))L/2
   = L-(c1+2(1/2))L/2
   = (1-(c1+1)/2)L
   = (1/2)(1/2)L = (1/4)L = c2L

n=3 ¿¡¼­,

a3 = L-(c1+c2+(1/2)+c2+(1/2)+(1/2))L/3
   = L-(c1+2c2+3(1/2))(L/3)
   = (3-c1-2c2-(3/2))(L/3)
   = ((3/2)-1)(L/3)
   = (1/2)(1/3)L = c3L

n=4 ¿¡¼­,

a4 = L-(c1+c2+c3+(1/2)+c2+c3+(1/2)+c3+(1/2)+(1/2))L/4
   = L-(L/4)(4*(1/2)+c1+2c2+3c3)
   = L-(L/4)(4*(1/2)+(1/2)+2(1/2)(1/2)+3(1/2)(1/3))
   = L-(L/4)(1/2)(4+1+1+1)
   = (4-(4+3)/2)(1/4)L
   = (1/2)(1/4)L = c4L

n=n ¿¡¼­,

an = L-(L/n)((n/2)+c1+2c2+3c3...(n-1)cn-1)
   = L-(L/n)((n/2)+(1/2)+2(1/2)(1/2)+3(1/2)(1/3)...(n-1)(1/2)(1/(n-1)))
   = L-(L/n)(1/2)(2n-1)
   = (n-(2n-1)/2)(1/n)L
   = (1/2)(1/n)L

ÀÌ µÈ´Ù.

*** Âü°í¹®Çå[References] ***

an = (1/2)*(1/n)*L
ÀÛ¼ºÀÚÀÇ ¼ö½Ä±×¸²ÀÌ ¾ø½À´Ï´Ù. No picture for this formula
º¯¼ö¸í Variable º¯¼ö°ª Value º¯ ¼ö ¼³ ¸í Description of the variable


¡Ø ÀÌ »çÀÌÆ®´Â ±¤°í¼öÀÍÀ¸·Î ¿î¿µµË´Ï´Ù.

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  • n °ª¿¡ µû¸¥ ÇÕÀ» ±¸ÇÏ´Â ½ÄÀº ¾ø±º¿ä.
    n=1 : ¥Òa = 1/2 = 0.5
    n=2 : ¥Òa = 1/2 + 1/4 = 0.75
    n=3 : ¥Òa = 1/2 + 1/4 + 1/6 = 0.917
    n=4 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 = 1.042
    n=5 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 = 1.142
    n=6 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 + 1/12 = 1.225
    n=7 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 + 1/12 + 1/14 = 1.296
    n=8 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 + 1/12 + 1/14 + 1/16 = 1.359
    n=9 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 + 1/12 + 1/14 + 1/16 + 1/18 = 1.414
    n=10 : ¥Òa = 1/2 + 1/4 + 1/6 + 1/8 +1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 = 1.464
    ÀÌ·¸°Ô µÇ´Â ±º¿ä. ¤¾¤¾¤¾

    aloha
    [2022-05-15 13:50:38]
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