Question

Tính tổng
A=1.3+2.4+3.5+...+99.101

Answer 1

A=1.3+2.4+3.5+....+99.101

A=1.(2+1)+2.(3+1)+.....+99.(100+1)

A=1.2+1+2.3+2+3.4+3+....+99.100+99

A=1.2+2.3+3.4+...+99.100+(1+2+3+4+....+99)

Đặt B=1.2+2.3+.....+99.100

=>3B=1.2.3+2.3.(4-1)+.....+99.100.(101-98)

=>3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+......+99.100.101-98.99.100

=>3B=99.100.101

=>B=33.100.101=333300

Đặt C=1+2+3+4..+99

=>C=(1+99).99:2=4950

=>A=333300+4950=338250

Answer 2

cam on