answer49 - 4901 a b c b b a 2 b 2 c 2 42< ab 9b 8c a b c...

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Unformatted text preview: 4901 a , b, c b b a 2 + b 2 + c 2 + 42 < ab + 9b + 8c a , b, c b a +b +c 2 2 2 + 42 b ab + 9b + 8c 2 a +b +c 2 2 2 2 + 43 ab + 9b + 8c a = 3, b = 6, c = 4 1 a- b 2 b + ] z ... 7 E ; @ ; @ E :u 0 ] + 3 4 ( b - 6) + ( c - 4) 2 = 0b 38y /* 12y /* a b c 31.6 a b c 4902 n y* b b b p 2 2.2 [2 1 4 :2 12 22 n2 1 1 1 + + ... + = p[ + + ... + ] 1 3 3 5 (2n - 1) (2n + 1) 1 3 3 5 (2n - 1) (2n + 1) p ' y n+1 2 p= 1.2 : 1 1 1 1 = ( - ) ( 2n - 1) ( 2n + 1) 2 2n - 1 2n + 1 = [( - ) + ( - ) + ... + ( : ]: p 1 2 1 1 3 1 3 1 5 1 1 p 1 1 np - )] = ( - )= 2 n - 1 2n + 1 2 1 2n + 1 2n + 1 n2 n2 1 1 1 1 1 1 = = [1 + ] = [1 + ( - )] 2 ( 2n - 1) ( 2n + 1) 4n - 1 4 ( 2n - 1) ( 2n + 1) 4 2 2n - 1 2 n + 1 1 1 2 1 1 3 1 4 1 1 2 3 1 5 1 4 1 1 1 - )] 2 2n - 1 2n + 1 = [1 + ( - )] + [1 + ( - )] + ... + [1 + ( = 4 [n + 2 ( 1 - 2n + 1 )] = 2( 2n + 1) 1 1 1 1 n( n + 1) [2 = [ = [ [2 : n2 1 n2 n2 = ( - ) ( 2n - 1) ( 2n + 1) 2 2n - 1 2n + 1 1 12 12 2 2 2 2 3 2 3 2 n2 n2 - + - + - + ... + - ] 2 1 3 3 5 5 7 2n - 1 2n + 1 n( n + 1) 1 n2 n 2 - ( n - 1) 2 1 12 2 2 - 12 3 2 - 2 2 n2 )] = + + + ... + - ] = [n - 2 2n + 1 2( 2n + 1) 2 1 3 5 2n - 1 2n + 1 : ( 2n - 1) ( 2n + 1) = 1 1 4 1 1 3 2 3 2 5 n2 1 (2 - 3 5 1 1 )( 2 + n ) n = 1 1 1 1 n n [ + ]= [ + ] 1 1 4 2- n 2+ n 4 2 n - 1 2n + 1 = [ + ( + ) + ( + ) + ... + ( n-1 n n + )+ ] 2n - 1 2n - 1 2n + 1 1 n 1 n n( n + 1) p p p 1p p = 4 [1 +p1 + 1 +p ... + 1 + 2n + 1 ] = 4 [n + 2n + 1 ] = 2( 2n + 1) np [2 2 1 : 1 1 1 1 1 = [ 1 3 + 3 5 + ... + ( 2n - 1) ( 2n + 1) ] +3 [ 3 5 + 5 7 + ... + ( 2n - 1) ( 2n + 1) ] + +5 [ 5 7 + 7 9 + ... + ( 2n - 1) ( 2n + 1) ] +...+ ( 2n - 1)[ ( 2n - 1) ( 2n + 1) ] = [( - = [n - [2 1 2 1 1 2 1 1 1 1 1 1 1 1 ) + 3( - ) + 5( - ) + ... + ( 2n - 1)( - )] 2n + 1 3 2n + 1 5 2n + 1 2n - 1 2n + 1 1 1 1 1 n( n + 1) 1 + 3 + 5 + ... + ( 2n - 1) 1 n2 ] = [n - ]= 2( 2n + 1) 2n + 1 2 2n + 1 : 1 2 2 3 n2 1 n( n + 1) n( n - 1) = [ - ] ( 2n - 1) ( 2n + 1) 2 2n + 1 2n - 1 6 5 2 3 n( n + 1) n( n + 1) n( n - 1) - )] = 2( 2n + 1) 2n + 1 2n - 1 [H L = [( - 0) + ( - ) + ... + ( ]: ^ (1)H L = 12 22 n2 + + ... + 1 3 3 5 ( 2n - 1) ( 2n + 1) = 2( 2n + 1) n( n + 1) [ (2)1.2 n=1 2 2.2 n=k HL * 3.2 n=k+1 2 [ 1 2 12 = 1 3 2 3 k ( k + 1) 12 22 k2 + + ... + = 2( 2k + 1) 1 3 3 5 ( 2k - 1) ( 2k + 1) ( k + 1) 2 12 22 k2 + + ... + ]+ 1 3 3 5 ( 2k - 1) ( 2k + 1) ( 2k + 1) ( 2k + 3) k ( k + 1) ( k + 1) 2 ( k + 1) + = [k ( 2k + 3) + 2( k + 1)] 2( 2k + 1) ( 2k + 1) ( 2k + 3) 2( 2k + 1) ( 2k + 3) = = 2( 2k + 1) ( 2k + 3) ( 2k + 1)( k + 2) = 2( 2k + 3) * E 9 ۸ 3.2 2 * n L L 1. 2 2. 2 3. B'@ >1~]+p;E 2 1. 2 2.E 9 `*2z]+8 9 @ E *L 3. L * 2 2 4903 12 L * E E 9 @ `*3z]+8 E E 9 @ `*4z]+8 2 * L * L *E 9 ` 2 E1.E; p9EP`м* 9 * 2. L 2 72 E; p * Y p 7 L E 9EP`м* 9 E 4@ @ 7[; * [ 72 32 62 12 12 22 A S *E 9 B ` C L CL / ( k + 1) ( k + 1)( k + 2) n( n + 1) np = 2( 2n + 1) 2n + 1 p= n + 1 2 p L *E 9 2 S 2@ E;@ E: S 13 6 +]z... 12 ܸ 13 2 L 2 2 X 2* L 2 6 +]z... 2 L 2 2 L 22 L 2 L 2* L 2 22 2 L 2 1111 6 + ] z ... A 2 B L * * B/ p6 Y C b 62 p;E 2 12 7 E ; @ E 9 xQ* + 4904 2 Ob Ab Bb Ob PQ b AP = BQ ` 9 E ; p + ] ~ 1 > 8Ƕ E 9 xQ* * ` P E 9 A B O 2 2 1.2 AO b 2.2 AB ƶ* 3.2 OQ b b AO = OA B A A AO = OA O b Q(2 Q ) PQ b Q' Q' 1 P O 2 Q A A'' O b Pb OP = OQ b b 1= 2 AOP A OQ (SAS 2 ) AP = AQ = BQ ض S X* E 9 b ض* * 8 * 916 ` R 4905 Ab Bb 11 913 * 2 * 82 914 (* Q 9 E 931 h* R 9 E 8 * 72 O pY* * 62 22 02 1 911 (* Q 9 E 816 h* R 9 E 2 (367367 + 762762)123123 ] * 2 717 7292 733 741 2 3674 3 367367 ] 212 2242 238 246 2 7624 2 762762 ] 1 2 3 4 762 3 3 3 92 3 7 3 1 2 1234 3 762 ] 9 367367 + 7627622 123123 3 4 7=49 ] ] 7[ @;E4 2 * * * * * ] Y pѼ*6 Y pѼ*6 Y pѼ*6 Y pѼ*6 76 ] 72 72 2 * 24 ] * 16 ] * 19 ] 62 12 02 32 3 4 7 ...
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This note was uploaded on 03/25/2011 for the course MATH 1232 taught by Professor Dr.jiangzhengchien during the Spring '11 term at Nanjing University.

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