Các bạn giúp mình giải bài toán này với: 1.Tính tổng: D= 1.99+2.98+3.97+...+98.2+99.1

Đáp án:

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 D=1.2+2.3+...+98.99

=>3D=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

=>D=98.99.100:3=323400

=>1.99+2.98+3.97+...+98.2+99.1=490050-323400=166650