answer73 - 7301 △ ˜¼lºª*ÐE 22 22∆333 3 3 33 50 3 2...

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Unformatted text preview: 7301 △ ˜¼lºª*ÐE 22 22∆333 3 3 33 50 3 2 50 3 3 73 7 | 111111 3 3 22 22∆333 3 = 22 22 × 10 53 + 22∆33 × 10 48 + 33 33 3 33 50 3 6 50 3 5 48 3 6 48 3 5 7 | 22 22 × 10 53 48 6 7 | 33 33 48 3 5 3 7 | 22∆33 7 | 22∆33 × 10 48 (7,10 48 ) = 1 3 22∆33 = 21028 + 1∆05 = 7 × 3004 + 1∆05 ∆=5 ªºYÆ 22 @) 7 E5 8 *ªºYƈ 7302 ¸ f * ª º Y ˜Æ nf f (n) f * ª n ÈF º 0ÌB´ª*6 [ f ( n) nf = 1f n f cf * f ª º n ˆÆ Y * ª º a ˜Æ Y * ª º b ˆÆ Y f ( n) = 1 ⇒ f (n) = n ⇒ a + b + c + ab + bc + ca + abc = 100a + 10b + c f n 99a + 9b − ab 3 a + b + ab 3 c ≤ 9 f 99a + 9b − ab ≤ 9(a + b + ab) 90a ≤ 10ab a ≥ 1f b ≥9f b = 9f 3 c= f * f ª º n ˜Æ Y 3 a = 1,2,* º ,9 ˆÆ ªY c= 90a + 81 = 9f 10a + 9 * ª º Y 9ˆ Æ 93 f ( n) = 1f n n = 199,299,399,499,599,699,799,899,999 f f f 11 6 á²Ô’+ 7303 7@E 5 8 2 @Eʳ 7 (lº 2 *ª B´ª* [ 0 È º *ª B´ª* [ 0 È º *ª B´ª* [ 0 È º *ª B´ª* [ 0 È º ²Ô’+ á ak f k8 a1 = 1, a 2 = 1, a3 = 2, a 4 = 3, l x 11235 610 600* m º Ø ª 8 13 21 34 15 55 89 144 233 377 610 7200 È 2È mºª* 7200÷12 600( ) 12 (l 12 (l 78 8Øm * º ª 600 * E ° `¸ Eª Ð 4*ت m º 578 15 غ m 8ª 7304 ʳ 3 △ ABC * mª Eغ fff ∠ Bf ∠C 8 f DM f DN AB f AC f E3 F3 D BC f N f Mf EF f A E M N F B D C mºª I f ∠IEFf ∠IAFf 0 A A IA f IE f IF f BM f CN f ∠A 2 ∠BEMf 9003 ∠C 90 3 2 0 0 Af Ef If F f ∠A 2 E ∠B ∠BICf 90 3 2 ∠A 90 3 2 M I N ∠BEM B F ∴Bf Ef Mf I f f ∠BMIf ∠BEIf 900 3 ∠BNCf 900 3 DM f DN Ⱥª mF ∴ DM f DN f [È ºª*ÀmC´ x ]h 'ºª* ʳ 1. 1 BC 2 * 3 13 If f I(0,0) I 3 x23 y23 △BMCf f △BNC f ]' BC 躪 D C A 2. 3. 4. EF f yf b △ABC 躪 ]' BC f Gf E( a,b)3 F(a,b)3 G(r,s)3 ⇒ E3 AB f f axf byf 1 3 F3 AC f axf byf 1 3 G3 BC f rxf syf 1 ∵ E∠ F è èè ∴ a23 b23 13 r23 s23 1 ⇒ a23 13 b2 r23 13 s23 1 ……(*) − ax + by = 1 b−s a+r B( , ) 3 f rb + as rb + as rx + sy = 1 ax + by = 1 b−s −a+r C( , ) 3 f rb − as rb − as rx + sy = 1 ∵D f BC f 1 b−s b−s 1 a+r −a+r + ], [ + ]) ∴ D( [ 2 rb + as rb − as 2 rb + as rb − as ⇒D( rb 1 + bs , ) b+s b+s E(- a, b) M P N ( I F( a, b) B D G( r , s ) C (*)3 5. b−s a+r y= x BI : rb + as rb + as 3 3 EF : y = b b−s −a+r y= x CI : rb − as rb − as 3 3 EF : y = b 3 P f MN f 1 b 2 − bs b 2 − bs P( [ + ], b) 2 a+r −a+r rb , b) ⇒P ( b+s N( b 2 − bs , b) a+r 6. 7. b 2 − bs M( , b) −a+r (*)3 8. 3 4.7. D P x= rb b+s ∵P f MN f ∴ DM f DN f 1. @ 7 E ∠P º q ˜ 2. 5 E @ 7 FÈ[ ºª ´ C m À * 3. Ø 3 73 á F 3 13 ‚ Ø DP ⊥ MN △∠ 3 ¸q ýº * ª 23 N + 13 7305 1∆ 2∆ 3∆ ⋅⋅⋅ ∆ 2008∆ 2009 = 1 ∆♠ ´ℵ∪ ≡ mª C[ * ∗ ? ≡ θ Ø ♠ ( i) 589 1 + 2 + 3 + ⋅⋅⋅ + 2008 + 2009 = 1 + 2009 × 2009 = 2019045 2 ¬ 2 1∆ 2∆ 3∆ ⋅⋅⋅ ∆ 2008∆ 2009 = 1 ¼ l 2019045 + 1 = 1009523 2 2,3, ⋅⋅⋅,2009Μ * Ð ª º4ο E 8 1009522(=1009523-1)'x ªº] (ii)E@ )7 3 (i @ 1422 + 1423 + ⋅⋅⋅ + 2009 = 2,3, ⋅⋅⋅,2009 1 xMo 1422 + 2009 × 588 = 1008714 < 1009522 2 ( 1009522 588 ) x E*Ѓ 8º X m ª 808 'x *º] ª 808 + 1422 + 1423 + ⋅⋅⋅ + 2009 = 808 + 1008714 = 1009522 ξ 588 ( ) 1 − 2 − 3 − − 807 + 808 − 809 − 810 − − 1421 + 1422 + 1423 + ⋅⋅⋅ + 2009 = 1 º m Ε o ∠ h♠ ∗ ( 589 ) 1.x]∗ ' º♠ ∅ ξ ™〈 + ″ 6 ] ' xº♠ ∗ 3 ≅ 7 2.@ #5 @ ]) E 8 ≅7 @5 @ E8 ]) ] ' xº♠ ∗ ≅ 7 3.@ 5 @ #8 ]) E µξ ≡ 15 3 7 º♠ Ε ∠ Xp Æ∗ 816 ∗ Ε o ∠ €º♠ M ξ214 ξ803 820 3 308 xº♠ ]' ∗ 1 m∠ ∗ Ε10 Pº♠ † 3 ≅ ≅ ≅ ' xº♠ ∗ Ε ∠ €º♠ mƒ ∗ ' xº♠ 3 ...
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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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