Question

B=1.1+2.2+3.3+...+20.20

Answer 1

B=1.1+2.2+3.3+...+20.20

=>B=1.(2-1)+2.(3-1)+3.(4-1)+...+20.(21-1)

=>B=1.2-1+2.3-2+3.4-3+.....+20.21-20

=>B=1.2+2.3+3.4+....+20.21-(1+2+3+4+5..+20)

Đặt A=1.2+2.3+..+20.21

=>3A=1.2.3+2.3.3+....+20.21.3

=>3A=1.2.3+2.3(4-1)+....+20.21.(22-19)

=>3A=1.2.3+2.3.4-1.2.3+....+20.21.22-19.20.21

=>3A=20.21.22

=>A=20.7.22=3080

Đặt M=1+2+3+...+20

=>M=(1+20).20:2=210

=>B=A-M=3080-210=2870

Vậy B=2870