Question

Tính tổng : S=1*2+2*3+3*4+....+99*100

Answer 1

\(3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

\(3S=1.2.3.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)

\(3S=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(3S=99.100.101\)

\(S=\frac{99.100.101}{3}\)

\(S=33.100.101\)

Answer 2

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

3S=1*2(3-0)+2*3(4-1)+3*4(5-2)+...+99*100(101-98)

3S=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+99*100*101-98*99*100

3S=99*100*101

S=(99*100*101):3

S=333 300