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¹«Çѱ޼ö Á¤¸® º¸°í¼­(¼öÇÐ)

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2017.12.28
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5 page / 21.5 KB
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 ¹«Çѱ޼ö Á¤¸® º¸°í¼­(¼öÇÐ) #4 ¹«Çѱ޼ö Á¤¸® º¸°í¼­(¼öÇÐ) #5

1Àå ¹«Çѱ޼ö․¾çÇ×±Þ¼ö
1. ¹«Çѱ޼ö
2. ¾çÇ×±Þ¼ö ÆÇÁ¤¹ý

2Àå ±³Ç×±Þ¼ö․¸è±Þ¼ö
1. ±³´ë(±³Ç×)±Þ¼ö
2. ¸è±Þ¼ö

3Àå TaylorÀÇ Á¤¸®․ÇÔ¼öÀÇ Àü°³
1. Taylor ±Þ¼ö
2. Maclaurin ±Þ¼ö
3. ¸è±Þ¼öÀÇ ÀÀ¿ë

¹«Çѱ޼ö  Á¦ 1 Àå ¹«Çѱ޼ö¾çÇ×±Þ¼ö  
¡×1.¹«Çѱ޼ö
  
(1) ¹«Çѱ޼öºÎºÐÇÕ
¹«ÇѼö¿­ÀÇ ÇÕÀ» ¹«Çѱ޼ö¶óÇÏ°í sumfromn1to¡ï a n
À¸·Î ³ªÅ¸³½´Ù.
¹«Çѱ޼ö¿¡¼­ ùÇ׺ÎÅÍ Á¦ nÇ× ±îÁöÀÇ ÇÕ s n sumfromk1ton a k
À» ÀÌ ±Þ¼öÀÇ ºÎºÐÇÕÀ̶ó°í ÇÑ´Ù.
(2) ¹«Çѱ޼öÀÇ ¼ö·Å¹ß»ê
¨çsumfromn1to¡ï a n  
ÀÌ a¿¡ ¼ö·Å ¢¢limfromn¡æ¡Ä`s n``limfromn¡æ¡Äsumfromk1ton a k``a
¹«Çѱ޼öÀÇ ÇÕÀº a  ¨è ¹«Çѱ޼ö sumfromn1to¡ï a n  ÀÌ ¼ö·ÅÇϸé, limfromn¡æ¡Ä a n``0  ( ¿ªÀº ¼º¸³ÇÏÁö ¾Ê´Â´Ù )  
(3) ¹«Çѵîºñ±Þ¼ö
µîºñ¼ö¿­ÀÌ ¹«Çѱ޼ö¸¦ ÀÌ·ê ¶§,  r < 1 ÀÏ ¶§ ¼ö·ÅÇϸç ÇÕÀÌ a over 1-r  ÀÌ°í,  
r 1 ÀÏ ¶§ ¹ß»êÇÏ°Ô µÈ´Ù.
¡×2.¾çÇ×±Þ¼ö ÆÇÁ¤¹ý
  
±Þ¼ö¸¦ ÀÌ·ç´Â °¢Ç×ÀÌ ¸ðµÎ ¾ç¼öÀÎ ±Þ¼ö¸¦ ¾çÇ×±Þ¼ö¶ó Çϸç, ¾çÇ×±Þ¼ö°¡ ¼ö·ÅÇϱâ À§ÇÑ ÇÊ¿äÃæºÐÁ¶°ÇÀº ºÎºÐÇÕÀÌ À¯°èÇÑ °ÍÀÌ´Ù.
(1) nÇ× ÆÇÁ¤¹ý
±Þ¼ö¸¦ ÀÌ·ç´Â ÀϹÝÇ×ÀÇ ±ØÇÑ°ªÀÌ 0ÀÌ ¾Æ´Ï¸é ±× ±Þ¼ö´Â ¹ß»êÇÑ´Ù
(2) ÀûºÐÆÇÁ¤¹ý (integral test)
¾çÇ×±Þ¼ö sumfromn1to¡Ä a n  ¿¡ ´ëÇÏ¿©, ÇÔ¼öf(x)  
°¡ [1,¡Ä)¿¡¼­ ¿¬¼ÓÀÌ°í ´ÜÁ¶°¨¼ÒÀÎ ¾çÀÇ ÇÔ¼öÀ̸ç, f(n) a n
(n¡Ã1) À̶ó ÇÒ ¶§, ÀÌ»óÀûºÐ integral from1to¡Ä f(x) dx
ÀÌ Á¸ÀçÇÏ¸é ±Þ¼ö´Â ¼ö·ÅÇÏ°í, Á¸ÀçÇÏÁö ¾ÊÀ¸¸é ±Þ¼öµµ ¹ß»êÇÑ´Ù.
¡Ølog  ¸¦ Æ÷ÇÔÇÑ ½Ä¿¡¼­ ÁÖ·Î »ç¿ëÇϸé ÁÁ´Ù  
(3) p-±Þ¼ö ÆÇÁ¤¹ý
sum from n1 to ¡Ä 1 over n^p``1 1 over 2^p 1 over 3^p.1 over n^p.
ÀÌ ¼ö·ÅÇϱâ À§ÇÑ ÇÊ¿äÃæºÐÁ¶°ÇÀº p > 1 ÀÌ´Ù.
p ¡Â 1ÀÏ ¶§´Â ¹ß»êÇÑ´Ù     (ÀÌÇÏ »ý·«)

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