Question

[hi]

C=1.99+2.98+3.97+...+98.2+99.1

Answer 1

[bảo nam trần]

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

Answer 2

[Quốc Đạt]

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