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14 tháng 6 2016

Ta có :

C = 1.99 + 2.(99 - 1) + 3.(99 - 2) + ... + 98.(99 - 97) + 99.(99 - 98)

C = 99.(1 + 2 + 3 + ... + 98 + 99) - (2 + 2.3 + 3.4 + ...+97.98 + 98.99)

C = 99.(1 + 99).99/2 - 98.99.100/3

C = 99.50.99 - 98.33.100

C = 490050 - 323400

C = 166650

14 tháng 6 2016

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 

C=1.99+2.98+3.97+98.2+99.1

C=(1x1x99x99)+(2x98x98x2)+3x97

C=9801+9604+291

C=19405+291

C=19696

13 tháng 6 2017

\(C=1.99+2.98+3.97+........+97.3+98.2+99.1\)

\(\Rightarrow C=1.99+2.\left(99-1\right)+3\left(99-2\right)+..........+98.\left(99-97\right)+99.\left(99-98\right)\)

\(\Rightarrow C=1.99+2.99-1.2+3.99-2.3+........+98.99-97.98+99.99-98.99\)

\(\Rightarrow C=\left(1.99+2.99+.......+99.99\right)-\left(1.2+2.3+.........+98.99\right)\)

\(\Rightarrow C=490050-\left(1.2+2.3+....+98.99\right)\)

Đặt \(A=1.2+2.3+3.4+........+98.99\)

\(\Rightarrow3A=1.2.3+2.3.3+..........+98.99.3\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+.....+98.99\left(100-97\right)\)

\(\Rightarrow3A=1.2.3-1.2.3+2.3.4-2.3.4+......+97.97.99-97.98.99+98.99.100\)

\(\Rightarrow3A=98.99.100\)

\(\Rightarrow A=\dfrac{98.99.100}{3}=323400\)

\(\Rightarrow C=490050-323400=166650\)

Vậy \(C=166650\)

13 tháng 6 2017

Xem lại đề đi bạn. Đề có vấn đề?!

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

17 tháng 5 2015

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

31 tháng 1 2016

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

31 tháng 1 2016

1,99+2,98+3,97+...+98,2+99,1 thì sẽ bằng => 166 650

5 tháng 1 2016

S = (50  -49)(50  +49) + (50 - 48)(50 + 48) + .... + (50 + 48)(50  -48)

S = 502 - 492 + 502 - 482 + ..... + 502 - 482 + 502 - 49

S = 99  . 502 - 2.(02 + 12  +.... + 492)

 

5 tháng 1 2016

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