Sáng kiến kinh nghiệm ngành sư phạm toán
!"#"$%$&' ()**+(,$"-.$ (/+(-#"$$ 012&324*+5+#! 6% (/7$899:;&<$!!"-9 59:()#! 6%=4 *+4>!()$9?$& @:A"A$()!"($BC28;; A$? ! 6%-(D(/ (B EF&G2 +96%!$& EH&,:9I$A$J6& EK&I2!:A$ #! ! & '$($59! $94(D!2 0L"C$A$ ? $-$?>$94+# #"$-C?J(/F2()9!M!! $94-$94(/>/;12()()? 29&' !!"59:! 6%(D 0-#NO94+!"J?PN$7#A$ ! !"Q $9:! 6%4+9R! 8"6(/:S$9TI2!:()& , - - !6()$"*S$9TI2 F + + = ! !6()*&'9%SA$+ H H H U V & = + + &I2!: - - & .+ - - $WA$ +! - & E J"-$?+N+96%Q(/ = -! H H H H α α = = & 'C8;5-$?+!"D#A$! ($ 3 X α > U>$V-4YZ[\Z H()-$? ( ) H H H H H H H H H H H H H H H α α α α α α + ≥ + ≥ + ≥ ,:5$J(/ H H H U V H U V H H H H α α α α + + + ≥ + + = ,> α $ & H α α + = $" F F ] H ^ α − + + = E#"$!1 H H H H F α α = = + + = $" ^ ^ F F ] F F ] H F ] = = + − + + = + _J F F ] 9 & H − + + = & , - - !6()S$9TI2 F + + = ! - ! ()%&'9%SA$+ H H H & = + + & Z:65CD#A$.! F-$8; - -F = + = + = + ? - - - - - !()Q>$& `4YZ[\Z H()-$? H H H H H H H - H - H & + ≥ + ≥ + ≥ ,:5-$J(/ H H H & ≥ + + E#"$!1 H H H H H H = = = $" H H H H H H & UFV = = ⇒ = = ,> - - - - - $ H = = = S$9TUFV& '$? UFV U VU VU V ⇔ + + + = ( ) H H U VU V U V H F H ⇔ + + + + = ⇔ + + + + + + + = ⇔ + + + + + + = ⇔ + + + = Z! a U VU V = 5 K & = E ? K H H U FV X UHV + + + − = bc!UHV?29()" X & 3J" X 9 H = X !29()"A$()UHV& .! F!.! H66?PN$$> - - 0 - - ! 02-9R!I2!:A$(/S$9T&,- $>9!$9 & @0 - - - H H H = = = $Q? F + + = -4! 9 .! F 0.! H$Q(/9:! 6% $9& G 0! - - - = = = $LQ?!: F + + = - ()6$LQ?9:! 6%$9 & @?-((d;A$.! F!.! H!98"69: ! 9$18"69:- 0(/S$ 9TI2!:()&'N C((d!"?+8" 6(/I! (& ! , F H - -&&&- ! 6 S$ 9T I 2 F H &&& X + + + = ! F H &&& F + + + = &'9%A$+ F ≤ < ≤ = − ∏ & " & e'(D/F& H = !(D/9(Df!"gF*- e'(D/H& K = -9;*7$#= F H K ≤ ≤ & `4YZ[\Z K89-$? K F H F K H K K F H F K H K K F U V U V H H U V U V H K H F ] − = − − − − + + − ≤ − = ≤ E ? F ^ ≤ #"$!1 F F H K K F F H K H K F K H F K H F X H F X F X H H = − + + = − = + + = ⇔ = − = − = = − ≥ & 3J" F 9$ ^ = & '(D/K& ^ = -9:65$6 9$ (/ F ^ H K = − = − 3# F H K ^ ≤ ≤ ≤ & @(J" H F ^ K − = − & @h92 H F ^ K − = − !)%!0 K H − = -$Q?:9! +9$S$9TI2 # K F K H ^ H ^ F H F ^ K F F H − − − − − = − = = = = + + + 'C8;5-D#A$! (D/ ^ = Q($ 3# F H K ^ ≤ ≤ ≤ -$? H F K F ^ F K H ^ H ^ K U VU VU VU VU VU V = − − − − − − E ? H K F K H ^ F ^ H H F ^ K a K F K H ^ F ^ H H F ^ K ^ F K H U HVU FV U V U V U V U V U V& & & & &U V F H F U V U V U V U V U V U V F H F a F F F F U V F F U V F H F a = + + − − − − = − − + + + − − − − − + + + + + − + + + ≤ − + + + − + + − + + + = a '$> X > $ F F F F F F F H F + + = − + + + + + $" H F& = − _?- F F F F K H F F F H F H + + = − + + = + + + !$(/ ( )( )( ) a F H K ^ H i K H &U V F H a H H F H F H − − + + ≤ ≤ − + $" ] F H ≤ #"$!1 F H K ^ F H K ^ F H K ^ K H K F ^ H ^ F H F ^ K X F X H F H H H F + + + = − − + + = + + + = − − − − − = − = = = = ≥ − + \#2()!"$J(/ ^ F K H H H ^ H ^ − = − = = − = _J ] F 9$ H = & e'(D/^& j = & 3# F H K ^ j ≤ ≤ ≤ ≤ -CD#A$(D/H!K-9: 65-$N$":+ 9$ ! j F ^ H K - - X = − = − = & E J" j ^ H F K H ^ K - - − = − − = − C?$?+ Jh9 2 H F − )%! K H − :+ 9$ #S$ I2 ^ K K H K F j K H F j H j F j ^ ^ H ^ F F F F H H F H F H H F − − − − − = = = = = + + − − − − − = = = = = + + + 'C8;5-D#A$! (D/ j = Q($ _9;*7-$#= F H K ^ j ≤ ≤ ≤ ≤ -C?"$ H F K F ^ F j F K H ^ H j H ^ K j K j ^ U VU VU VU VU V U VU VU VU VU V = − − − − − − − − − − kl+ H K H ^ U FV UH FV = + + 3( K F j F K H H F ^ F j H ^ K j K j ^ ^ H U V U V U V U V U V & & & & F F H F H H U V U V U V U V U V & & & & H H F F F − − − − − = + + + − − − − − + + `4YZ−\Z FX89-$? K F j F K H H F ^ F FX FX j H ^ K j K j ^ ^ H FX j F ^ H FX U V U V U V F U V U V F F H F H H FX U V U V U V U V U V H H F F F F F K F K U V F U V F H F HU FV H F H FX − − − − − ≤ + + + + + + + + − − − − − + + + + + + + = − + + + − − + + + + + ,> X > $ F K F K F F H F HU FV H F H + + = − + + + + + $" F H = &_?- F K F K j F F H F HU FV H F H H ^ Hm + + = − + + = + + + = 'C8"-$(/ FX F H ^ j FX HX F j F & &U V H FX H ≤ − − + + ≤ E ? HH Hm H ≤ #"$!1 ! F H K ^ j F H ^ j F H K ^ j K F j F ^ F H F K H j H j K ^ H ^ K j ^ X F HU V HU V K H K HU V HU V X H K + + + + = − − + + = + + + + = − − − − = = = = − = − − = − = = − = = − ≥ \#2()!"$J(/ F j H ^ K K ] F ] X = − = − = − = − = & _J HH Hm 9$ H = & .()()6Q9(/D#A$! na& $%&'()*+,- , - - !:!$A$9:$9 (!$9 >& '9%SA$+ & & & = kl+ F & & = = & .! T ()()99$A$ & _"+ -;I$LN7h: & & & F + + = 3!C8"-$N$"!!"?+oYZ[\Z":- ? $($! $9() - - U>$V$ $ U & V &U & V &U & V U V &U V &U V & + + + = = '$#> - - $ F &U V H F &U V H F &U V H = + − + = + = ⇔ = − + + + = = − + & 'C8"-$? & & & & & = `4,$"":-$? F & & & & U V F U V + + + + + + ≤ ≤ + + + + = + + E ? U V + + ≤ + + p"$ U V U V U V U V U V + + + + − + + − + + − + + + + ≥ = − + + − + + − #"$!1 & & & = = & G$"