Question

Tính gái trị biểu  thức
A = 1.2+2.3+3.4+.....+99.100

\(B=1^2+2^2+3^2+......+99^2+100^2\)

Answer 1

3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

     = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - ... - 98.99.100 + 99.100.101

     = 99.100.101

A=333300

B= (1.2 + 2.3 + 3.4 + ... + 100.101) - (1 + 2 + 3+ 4 + ... + 100)

  = 333300 + 10100 - 5050

  = 333300 + 5050

  = 338350

Answer 2

A =  1*2 + 2*3 + 3*4 + ........+ 99*100

=>3A=1.2.3+2.3.3+3.4.3+...+99.100.3

<=> 3A =1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

<=> 3A =1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100

<=> 3A = 99.100.101 = 999900

=> S = 333300