Đặt 1.2 + 3.4 + 5.6 + ... + 99.100 là S, ta có:
S = 1.2 + 3.4 + 5.6 + ... + 99.100
3S = 1.2.3 + 3.4.3 + 5.6.3 + ... + 99.100.3
3S = 1.2.3 + 3.4.(5 - 2) + 5.6.(7 - 4) + ... + 99.100. (101 - 98)
3S = 1.2.3 + 3.4.5 - 3.4.2 + 5.6.7 - 5.6.4 + ... + 99.100.101 - 99.100.98
3S = 1.2.3 + 99.100.101
3S = 2.3 + 3.33.10100
3S = 2.3 + 3.333300
3S = 3.(2 + 333300)
3S = 3. 333302
S = 3.333302 : 3
=> S = 333302
Đặt \(A=\text{1.2+3.4+...+99.100}\)
\(3A=1.2.3+2.3.4+3.4.3+...+99.100.3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)....99.100.\left(101-98\right)\)
\(3A=\left(1.2.3+2.3.4+3.4.5+...+98.99.100\right)-\left(0.1.2+1.2.3+2.3.4+...+98.99.100\right)\)
\(3A=99.100.101-0.1.2\)
\(3A=999900-0\)
\(3A=999900\)
\(A=999900:3\)
=> \(A=333300\)
Vậy: \(\text{1.2+3.4+...+99.100 = 333300}\)
đề sai rùi bạn ơi
phải là tính :1.2+2.3+........+99.100
