Question

1²⁺2²⁺3²+4²+...+100²

Answer 1

 A= 1²+2²+3²+4²+.....+99²+100²

A =1.(2-1)+2.(3-1)+3.(4-1)+....+99.(100-1)+100.(101-1)

=1.2-1.1+2.3-1.2+3.4-1.3+...+99.100-1.99+100.101-1.100

=(1.2+2.3+3.4+...+99.100+100.101)-(1+2+3+...+100)

A= [1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99) ] /3 + [(100+1).100 /2]

=[1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+100.101.102-99.10.101]/3 + 5050

=100.101.102/3 + 5050

=348450

Answer 2

1²+2²+.......+100²

=1.(2-1)+2.(3-1)+..........+100.(101-1)

=1.2-1+2.3-2+..............+100.101-100

=(1.2+2.3+........+100.101)-(1+2+........+100){*}

Đặt S=1.2+2.3+........+100.101

3S=1.2.3+2.3.(4-1)+........+100.101.(102-99)

3S=1.2.3+2.3.4-1.2.3+.....+100.101.102-99.100.101

3S=100.101.102

S=100.101.102:3

S=343400

Thay vào {*}

Bạn tự làm tiếp

Answer 3

 A= 1²+2²+3²+4²+.....+99²+100²

A =1.(2-1)+2.(3-1)+3.(4-1)+....+99.(100-1)+100.(101-1)

=1.2-1.1+2.3-1.2+3.4-1.3+...+99.100-1.99+100.101-1.100

=(1.2+2.3+3.4+...+99.100+100.101)-(1+2+3+...+100)

A= [1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99) ] /3 + [(100+1).100 /2]

=[1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+100.101.102-99.10.101]/3 + 5050

=100.101.102/3 + 5050

=348450