cho A=1.99 + 2.98 + 3.97 + ..... + 99.1
và B= 1.101+2.102+3.103+.....+9.199
tính A+B
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A+B = (1.99+2.98+3.97+...+99.1)+(1.101+2.102+3.103+...+99.199)
A+B = (1.99+1.101)+(2.98+2.102)+(3.97+3.103)+...+(99.1+99.199)
A+B = 1(99+101) + 2(98+102) + 3(97.103)+...+99(1+199)
A+B = 1.200 + 2.200 + 3.200 +...+ 99.200
A+B = 200.(1+2+3+...+200)
A+B = 200.4950
A+B = 990000
A + B = ( 1 . 99 + 2 . 98 + 3 . 97 + ... + 99 . 1 ) + ( 1 . 101 + 2 . 102 + 3 . 103 + ... + 99 . 199 )
A + B = 99 . ( 1 + 199 ) + 98 . ( 2 + 198 ) + 97 . ( 3 + 197 ) + ... + 2 . ( 102 + 98 ) + 1 . ( 99 + 101 )
A + B = 99 . 200 + 98 . 200 + 97 . 200 + ... + 2 . 200 + 1 . 200
A + B = ( 99 + 98 + 97 + ... + 2 + 1 ) . 200
A + B = 4950 . 200
A + B = 990000
A+B=(1.99+2.98+...+99.1)+(1.101+2.102+...+99.199)
=(1.99+1.101)+(2.98+2.102)+...+(99.1+99.199)
=1.(99+101)+2.(98+102)+...+99(1+199)
=200+2.200+...+99.200
=200.(1+2+3+4+...+99)
=200.4950
=.....
1.99+2.98+3.97+...+98.2+99.1=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99.(99-98)
=1.99+2.99-1.2+3.99-2.3+...+98.99-97.98+99.99-98.99
=(1.99+2.99+3.99+...+98.99+99.99)-(1.2+2.3+3.4+...+98.99)
=99.(1+2+...+99)-(1.2+2.3+...+98.99)=99.4950-(1.2+2.3+...+98.99)=490050-(1.2+2.3+...+98.99)
đặt A=1.2+2.3+...+98.99
=>3A=1.2.3+2.3.3+...+98.99.3
=1.2.3+2.3.(4-1)+...+98.99.(100-97)
=1.2.3-1.2.3+2.3.4-2.3.4+...+97.98.99-97.98.99+98.99.100=98.99.100
=>A=98.99.100:3=323400
=>1.99+2.98+3.97+...+98.2+99.1=490050-323400=166650
1.99+2.98+3.97+4.96+...+98.2+99.1
=1.99+2.(99-1)+3.(99-2)+...+98.(99-97)+99.(99-98)
=1.99+2.99-1.2+3.99-2.3+...+98.99-97.98+99.99-98.99
=(1.99+2.99+3.99+4.99+...+98.99+99.99)-(1.2+2.3+3.4+...+97.98+98.99)
=(1+2+3+4+...+98+99).99-(98.99.100)/3
={(99-1+1)/2}.100.99-(98.99.100)/3
=49,5.100.99-(98.99.100)/3
=4950.99-(98.99.100)/3
=4950.3.33-98.100.33
B=14850.33-9800.33
B=(14850-9800).33
B=5050.33
B=166650