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ret hiperharmonis EMBED Equation.3 yang konvergen maka EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 Jadi untuk x = ½ deret konvergen.Untuk x = ½ deret menjadi EMBED Equation.3 = EMBED Equation.3 = EMBED Equation.3dengan Test Liebniz: a). EMBED Equation.3 EMBED Equation.3 b) | un+1 | = EMBED Equation.3 EMBED Equation.3 < | un |= EMBED Equation.3 n e" 1 J a d i u n t u k x = ½ d e r e t E M B E D E q u a t i o n . 3 j u g a k o n v e r g e n / / / K e s i m p u l a n . : D e r e t k o n v e r g e n ½ d" x d" ½ D e r e t d i v e r g e n x
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? i Í Î ø > ¦ X ÷ ì ì ì ì à Õ à à Í Í Í Á Á Á Á Á ¹ - - h dh ̂ h gdtu® dh gduL¥ h dh ̂ h gduL¥ dh gdÔ c & F dh gd =H h dh ̂ h gd =H & F dh gd Vò dh gd Vò O Q l m t u ¤ ¥ ¬ - À Á Â Ã Ä Î Ï â ã ä å ð ñ
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t ¡ ¢ £ ¤ Ê Ë à á ô õ ö ÷ ø ðßÓËÓ˼«ÓË£££yh£Ë££YH£ ! j]w hYgä hYgä CJ EHèÿU aJ jc¹I hYgä CJ U V aJ ! j.t h}I; hYgä CJ EHèÿU aJ jÅa¹I hYgä CJ U V aJ j hYgä CJ U aJ h°} hYgä CJ aJ mH sH hYgä CJ aJ ! jq h}I; hYgä CJ EHäÿU aJ j c¹I hYgä CJ U V aJ hj 4 CJ aJ j hj 4 CJ U aJ ! jn h}I; hYgä CJ EHèÿU aJ j×b¹I hYgä CJ U V aJ ø ù ! 4 5 6 7 8 9 [ \ d e x y z { | ~ ª « ¾ ¿ À Á Â Å Æ òêÞêϾÞêòêµêÞê¦ÞòêµêvÞgVÞòv ! jÎ} hYgä hYgä C hYgä CJ U V aJ h°} hYgä CJ H* aJ mH sH h°} hYgä CJ aJ mH sH ! j£{ hYgä hYgä CJ EHèÿU aJ jìc¹I hYgä CJ U V aJ hYgä CJ H* aJ ! jxy hYgä hYgä CJ EHèÿU aJ j¿c¹I hYgä CJ U V aJ j hYgä CJ U aJ hYgä CJ aJ j èð hYgä hYgä CJ aJ ! 3 4 5 6 7 F J M N a b c d e ¢ £ øðøäøÕÄä¹øðøäøª
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h Ú CJ aJ hvÅ CJ aJ h°} hvÅ CJ H* aJ mH sH h°} hvÅ CJ aJ mH sH h ̂ þ CJ aJ ! jö h}I; h Ú CJ EHäÿU aJ jf¹I h Ú CJ U V aJ h}I; h}I; CJ aJ ! jù h}I; h Ú CJ EHèÿU aJ jvf¹I h Ú CJ U V aJ j hYgä CJ U aJ hPC, CJ aJ hYgä CJ aJ £ © ̄ ¼ ¾ ¿ À Ò Ö ã å ç è # * + 3 5 7 8 ;
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) 2 C D K X Y l m n o r s t ̄ ° Ã Ä Å Æ Ï Ò Ó ú ñâÓñÓǸ©ÇÓâǸxÇÓâ¸Ç¸iXǸÓâ ̧ ! jz hÄSk hÄSk CJ EHèÿU aJ jZh¹I hÄSk CJ U V aJ ! jµ h QX hÿ#CJ EHäÿU aJ j h¹I hÿ#CJ U V aJ ! j h QX hÿ#CJ EHäÿU aJ jh¹I hÿ#CJ U V aJ h°} hÄSk CJ aJ mH sH j hÄSk CJ U aJ h°} hÉ CJ aJ mH sH h°} h Ol CJ aJ mH sH h°} hsvµ CJ aJ mH sH ú û ý T T U U ïàÑÏÀàѱ© © ©© hd m CJ aJ hÈ ³ CJ aJ hb'2 5CJ aJ hb'2 CJ aJ h cë 5CJ aJ h cë CJ aJ h°} h cë CJ aJ mH sH h LINKINTERNAL LINK EKSTERNALLINK DOKUMEN :Murray R. Spiqel JR, KALKULUS LANJUTAN, , Erlangga ,Jakarta 1991Purcel,E.J., Calculus With Analytic Geometry, Prentice Hall , Inc., 1994. kT ¢T ́ T îT U U U U U U ô è ô è ã ã ã ã Û $ a$ gd,3 gd cë h dh ̂ h gdb'2 & F dh gdb'2 , 1h °Ð/ °à=!° "° # $ %° °Ð °Ð
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! " # $ % & ' ( ) * + , þÿÿÿ. / 0 1 2 3 4 ýÿÿÿ7 : b ? A @ B D C E G F H I J L K M O N P Q R T S U V W Y X Z [ \ ̂ ] _ ̀ a c d f e g h i j k m l n p o q ÿÿÿÿÿÿÿÿÿÿÿÿ Ã W o r d D o c u m e n t ù ÿÿÿÿÿÿÿÿ .X O b j e c t P o o l ü ÿÿÿÿ påBÊ Î ý\Ê Î _ 1 2 3 6 8 7 5 6 8 6 ÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j ÿÿÿÿ f O b j I n f o ÿÿÿÿ ÿÿÿÿ þÿÿÿ þÿÿÿþÿÿÿþÿÿÿþÿÿÿ þÿÿÿþÿÿÿ þÿÿÿþÿÿÿ þÿÿÿþÿÿÿ þÿÿÿþÿÿÿ þÿÿÿþÿÿÿþÿÿÿþÿÿÿ þÿÿÿþÿÿÿþÿÿÿþÿÿÿ þÿÿÿþÿÿÿ! " þÿÿÿþÿÿÿ% þÿÿÿþÿÿÿþÿÿÿþÿÿÿ* þÿÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ 4 _ 1 2 3 6 8 8 3 3 8 4 T O Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j
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ÿÿÿÿ f O b j I n f o ÿÿÿÿ ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ F _ 1 2 3 6 8 8 3 8 5 4 ÿÿÿÿÿÿÿÿ Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ PÁ* µ ø
n = 0 " " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁw R ôb
+ ' l i m C o m p O b j ÿÿÿÿ
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f O b j I n f o ÿÿÿÿ ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ _ 1 2 3 6 8 8 3 8 1 3 ÿÿÿÿÿÿÿÿ Î À F påBÊ Î påBÊ Î n ! " C n + 1 C n = L þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ øÊ tø
1 L O l e ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j ÿÿÿÿ f O b j I n f o ÿÿÿÿ ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ 6 _ 1 2 3 6 8 8 3 8 3 0 Î À F påBÊ ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j ÿÿÿÿ f O b j I n f o ÿÿÿÿ ÿÿÿÿ þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ øÊ tø
1 L þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ 6 _ 1 2 3 6 8 8 3 9 2 0 ' Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j ÿÿÿÿ f O b j I n f o ÿÿÿÿ! ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ _ 1 2 3 6 8 8 3 9 5 2 ÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿ # PÁw S ìR
+ ' l i m n ! " C n C n + 1 = Á þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ 9 ,Ï
Á C o m p O b j # % ÿÿÿÿ $ f O b j I n f o ÿÿÿÿ& ÿÿÿÿ & E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ ' ) _ 1 2 3 6 8 8 3 9 6 4 " J ) Î À F påBÊ Î ÿÿÿÿÿÿÿÿÿÿÿÿ ( C o m p O b j ( * ÿÿÿÿ ) f O b j I n f o ÿÿÿÿ+ ÿÿÿÿ + E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ , ) þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ ئ :
Á þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ @ò ¤ù
2 n " 1 x n n 2 + 1 E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ 1 ) _ 1 2 3 6 8 8 4 2 6 0 , 6 3 Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ 2 C o m p O b j 2 4 ÿÿÿÿ 3 f O b j I n f o ÿÿÿÿ5 ÿÿÿÿ 5 E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ 6 _ 1 2 3 6 8 8 4 3 5 5 ÿ ÿÿÿÿÿÿÿÿÿÿÿÿ 9 n = 1 " " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ{ ¾ ́ õ
+ Á = ' l i m n ! " C n C n + 1 = C o m p O b j 7 9 ÿÿÿÿ : f O b j I n f o ÿÿÿÿ: ÿÿÿÿ
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DS Equation Equation.3 ô9²q PÁ, 8Å Ôæ
' l i m n ! " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Eq_ 1 2 3 6 8 8 5 7 0 1 ¤ ³ B Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ F C o m p O b j A C ÿÿÿÿ G f O b j I n f o ÿÿÿÿD ÿÿÿÿ I uation Equation.3 ô9²q PÁN Ø
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ò
2 n " 1 ( n 2 + 1 ) þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ J j _ 1 2 3 6 8 8 5 7 1 9 ÿÿÿÿ® G Î À F påBÊ Î påBÊ Î ÿÿÿÿÿÿÿÿÿÿÿÿ L C o m p O b j F H ÿÿÿÿ M f O b j I n f o ÿÿÿÿI ÿÿÿÿ O E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ P i _ 1 2 3 6 8 8 4 6 8 2 1 ÿÿÿÿÿÿÿÿÿÿÿÿ R PÁM ÈH ä³
( n + 1 ) 2 + 1 2 n þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ ̀ K è
2 n " 1 ( 1 / 2 ) n n 2 + C o m p O b j K M ÿÿÿÿ S f O b j I n f o ÿÿÿÿN ÿÿÿÿ U E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ V - _ 1 2 3 6 8 8 4 7 2 4 Q Î À F påBÊ Î p " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q O b j I n f o ÿÿÿÿ] ÿÿÿÿ i E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ j _ 1 2 3 6 8 8 4 8 3 1 ÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿ m C o m p O b j _ a ÿÿÿÿ n f O b j I n f o ÿÿÿÿb ÿÿÿÿ p E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ q Ñ _ 1 2 3 6 8 8 4 8 4 5 ̂
+ ' l i m n ! " 1 / ( 2 ( n 2 + 1 ) ) 1 / n 2 = þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q O l e ÿÿÿÿÿÿÿÿÿÿÿÿ u C o m p O b j d f ÿÿÿÿ v f O b j I n f o ÿÿÿÿg ÿÿÿÿ x E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ y É PÁ- ̂ ,Ð
+ ' l i m n ! " n 2 2 ( n 2 + 1 ) = 1 2 `" 0 þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁL °þ ß
+ n ! " l C o m p O b j s u ÿÿÿÿ f O b j I n f o ÿÿÿÿv ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ h _ 1 2 3 6 8 8 5 0 0 5 ÿÿÿÿÿÿÿÿy Î À | = þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ¬ % l_
+ ' l i m n ! " | ( " 1 ) n 2 ( n 2 + 1 ) | = O l e ÿÿÿÿÿÿÿÿÿÿÿÿ C o m p O b j x z ÿÿÿÿ f O b j I n f o ÿÿÿÿ{ ÿÿÿÿ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ È 0 þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Eq O b j I n f o ÿÿÿÿ ÿÿÿÿ ¤ E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ ¥ # _ 1 2 3 6 8 8 5 0 7 3 w | Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ ¦ C o m p O b j ÿÿÿÿ § f O b j I n f o ÿÿÿÿ ÿÿÿÿ © E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ ª _ 1 2 3 6 8 8 5 1 4 0 m
( " 1 ) n 2 ( n 2 + 1 ) ì ì þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q O l e ÿÿÿÿÿÿÿÿÿÿÿÿ - C o m p O b j ÿÿÿÿ ® f O b j I n f o ÿÿÿÿ ÿÿÿÿ ° E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ ± PÁ l_
( " 1 ) n 2 ( n 2 + 1 ) n = 1 " " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ; (ð ó
( 2 n + 1 ) ! 1 C o m p O b j ÿÿÿÿ Â f O b j I n f o ÿÿÿÿ ÿÿÿÿ Ä E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ Å W _ 1 2 3 6 8 8 5 6 0 ÿÿÿÿÿÿÿÿÿÿÿÿ Ç C o m p O b j ¢ ÿÿÿÿ È f O b j I n f o ÿÿÿÿ£ ÿÿÿÿ Ê E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ Ë ) þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ 8 lV
" þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q _ 1 2 3 6 8 8 5 6 4 9 ÿÿÿÿ© ¦ Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ Ì C o m p O b j ¥ § ÿÿÿÿ Í f O b j I n f o ÿÿÿÿ ̈ ÿÿÿÿ Ï E q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ Ð ) _ 1 2 3 6 8 8 5 6 6 1 ÿ ÿÿÿÿÿÿÿÿÿÿÿÿ Ñ C o m p O b j ª ¬ ÿÿÿÿ Ò f PÁ
" þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁ |
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" þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Equation Equation.3 ô9²q PÁy 0© ôb
f n ( a ) n ! ( x " a ) n n = 0 " " þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS Eq_ 1 2 3 6 8 8 6 2 3 1 ÿÿÿÿÿÿÿÿº Î À F ̀ /EÊ Î ̀ /EÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ æ C o m p O b j ¹ » ÿÿÿÿ ç f O b j I n f o ÿÿÿÿ¼ ÿÿÿÿ é uation Equation.3 ô9²q PÁÚ àï ß
f ' ( 0 ) 1 ! x + f " ( 0 ) 2 ! x 2 + f 3 ( 0 ) 3 ! x 3 + . . . . . . . . . þÿ ÿÿÿÿ Î À F Microsoft Equation 3.0
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DS EqE q u a t i o n N a t i v e ÿÿÿÿÿÿÿÿÿÿÿÿ ê ö _ 1 2 3 6 8 8 6 2 7 3 @ Ñ ¿ Î À F påBÊ Î påBÊ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ î C o m p O b j ¾ À ÿÿÿÿ ï f uation Equation.3 ô9²q PÁi