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    ( ) :"3 100" n P n n< + 1, 2,3, 4,5n =   ( ) :"2 " n Q n n< ! "#$%#&'( # )#*#++, -./$%&0%&1 * n N∈ 1 ! "2$%2&'( 2 )2*#++,%3&0%2&'2 2 42,%3& 0%#&'2 # 4#,%3& %3& ! "($%(&'( ( )(*#++,%3&0%(&'2 ( 4(,%3& ! "5$%5&'( 5 )5*#++,%3&0%5&'2 5 45,%3& ! "6$%#&'( 6 )6*#++,%7&0%6&'2 6 46,%3& 1   $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB BC$%& * n N∈ ! DE2;F$%& %$%G&.HIJHKL& BC$%& Phương pháp qui nạp ! DE#MN$%&"# 1n k= ≥ 1n k= + I. PHƯƠNG PHÁP QUY NẠP TOÁN HỌC   I. PHƯƠNG PHÁP QUY NẠP TOÁN HỌC: BC$%& Phương pháp qui nạp ! DE#MN$%& "# ! DE2;F$%&  %$%G&.HIJH KL& BC$%& II. VÍ DỤ: Vd1BCO/ #*(*6*PQ*%2R#&" 2 %#& * n N∈ $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB 1n k= ≥ 1n k= + * n N∈ "##"# 2 "2#*("2 2 "(#*(*6"( 2 PPPPPPPPPPPPPQ "G#*(*6*P*%2GR#&"G 2 "G*##*(*6*P*%2GR#& *S2%G*#&R#T"%G*#& 2 Hoạt động nhóm BCO./  * n N∈ ( 1) 1 2 3 2 n n n + + + + + = :U#2DE#  :U(5DE2%IJHKL&  :U6VDE2%WHLBC1& %#&   I. PHƯƠNG PHÁP QUY NẠP TOÁN HỌC: BC$%& Phương pháp qui nạp ! DE#MN$%& "# ! DE2;F$%&  %$%G&.HIJH KL& BC$%& II. VÍ DỤ: * n N∈ $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB 1n k= ≥ 1n k= + Hoạt động nhóm BCO./ * n N∈ ( 1) 1 2 3 2 n n n + + + + + = Giải: 3X n S VT= DE#: -"#/#"#W%#&3 DE2;Y%#& (1) 1n k= ≥ Q:Z ( 1) 1 2 3 . 2 k k k S k + = + + + + = %JHKL& LBC%#& 1n k= + [ 1 ( 1)( 2) 1 2 3 . ( 1) 2 k k k S k k + + + = + + + + + + = \\ 1 ( 1) ( 1) ( 1) 2 k k k k S S k k + + = + + = + + ( ) ( ) ( ) 1 2 1 1 2 2 k k k k + +   = + + =  ÷   -\%#& * n N∈   I. PHƯƠNG PHÁP QUY NẠP TOÁN HỌC: BC$%& Phương pháp qui nạp ! DE#MN$%& "# ! DE2;F$%&  %$%G&.HIJH KL& BC$%& II. VÍ DỤ: Vd1BCO/ #*(*6*PQ*%2R#&" 2 %#& * n N∈ $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB 1n k= ≥ 1n k= + * n N∈ Vd2BCO/ I]( * n N∈ 3 n n− Giải: 3X 3 n A n n= − Bư0c 1: -"#U 1 0 3A = M Bư0c 2:;Y"GU ( ) 3 3 k A k k= − M %JHKL& LBC 1 3 k A + M \\ ( ) ( ) 3 1 1 1 k A k k + = + + + 3 2 3 3 1 1k k k k= + + + − − 3 2 3 3 ( ) 3( )k k k k= − + + M M 14 2 43 14 2 43 1 3 k A + ⇒ M -\I]( 3 n n− * n N∈   BC$%& Phương pháp qui nạp ! DE#MN$%& "# ! DE2;F$%&  %$%G&.HIJH KL& BC$%& 1n k= ≥ $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB * Ch3 4: BC$%& %L^_`W& Phương pháp qui nạp ! DE#MN$%&  ! DE2;F$%&  %$%G&.HIJH KL& BC$%& n p≥ 1n k= + 1n k= + n k p= ≥ "L "L n k p= ≥ * n N∈   $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB * Ch3 4: BC$%& %L^_`W& Phương pháp qui nạp ! DE#MN$%&  ! DE2;F$%&  %$%G&.HIJH KL& BC$%& n p≥ 1n k= + "L n k p= ≥ ]K^U B]_(  a &7](  aG"#2(56 b&c`]GIJHdJH[ beLEfLLJHKL  (  1 a # 2 ( 5 6 ; & b&MIJH(  4a. 3n ≥ ( a ) g #V ) 2h 4 25 a# 4 (2 25( 4 5+ * n N∈   $89:;$<$0=>:?$@<:AB $89:;$<$0=>:?$@<:AB * Ch3 4: BC$%& %L^_`W& Phương pháp qui nạp ! DE#MN$%&  ! DE2;F$%&  %$%G&.HIJH KL& BC$%& n p≥ 1n k= + "L n k p= ≥ ]K^U B]_(  a &7](  aG"#2(56 b&c`]GIJHdJH[ beLEfLLJHKL ; b&MIJH(  4a. 3n ≥ DE#-"(/( ( 4aQ( W$%#& 3X$%&'(  4a,. DE2;YQ  3n k= ≥ LBC"G*#Q :Z( G 4aG%JHKL& [( G*# 4a%G*#& -\(4a. 1 0 0 3 8( 1) 3 .3 8 8 (3 8 ) 2.3 8 0 k k k k k k k + > > > + ⇔ > + ⇔ − + − > 14 2 43 14 2 43 3n ≥ 3n ≥ \\   . DE2;Y%#& (1)  1n k= ≥ Q:Z ( 1) 1 2 3 . 2 k k k S k + = + + + + = %JHKL& LBC%#& 1n k= + [ 1 ( 1) ( 2) 1 2. 1) ( 2) 1 2 3 . ( 1) 2 k k k S k k + + + = + + + + + + =  1 ( 1) ( 1) ( 1) 2 k k k k S S k k + + = + + = + + ( ) ( ) ( ) 1 2 1 1 2 2 k k k k +

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