Question

[Lê Thành Đạt]

Cho A = 1² +2² +3²+...+100² và B = 1.2+2.3+...+99.100.Khi đó A-B là?

Answer 1

[doremon]

A = 1² + 2² + 3² + ....+ 100²

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

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

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

   = B + 10100 -  \(\frac{\left(100+1\right)100}{2}\)= B +5050 5050

=> A - B = B + 5050 - B = 5050