đặt \(A=1.2+2.3+...+98.99\)
\(=>3A=3.1.2+3.2.3+...+3.98.99\)
\(=>3A=\left(3-0\right).1.2+\left(4-1\right).2.3+...+\left(100-97\right).98.99\)
\(=>3A=3.1.2-0.1.2+4.2.3-1.2.3+...+100.98.99-97.98.99\)
\(=>3A=-0.1.2+98.99.100\)
\(=>3A=98.99.100\)
\(=>A=\frac{98.99.100}{3}\)
Gọi đề bài là S .Ta có:
S = 1 x 2 + 2 x 3 + ... + 99 x 100
3S = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ..... + 99 x 100 x (101 - 98)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + .... + 99 x 100 x 101 - 98 x 99 x 100
3S = 99 x 100 x 101 = 999900
S = 999900 : 3 = 333300
\(A=1.2+2.3+3.4+...+98.99\)
\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+98.99.3\)
\(=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+97.98.\left(99-96\right)+98.99.\left(100-97\right)\)
\(=1.2.3-0+2.3.4-1.2.3+3.4.5-2.3.4+...+97.98.99-96.97.98+98.99.100-97.98.99\)\(=98.99.100\)
\(=970200\)
\(\Rightarrow A=\frac{970200}{3}=323400\)
Đặt A=1.2+2.3+...+98.99
=>3A=3.1.2+3.2.3+...+3.98.99
=>3A=(3−0).1.2+(4−1).2.3+...+(100−97).98.99
=>3A=3.1.2−0.1.2+4.2.3−1.2.3+...+100.98.99−97.98.99
=>3A=−0.1.2+98.99.100
=>3A=98.99.100
=>A=98.99.100/3
