Question

tính: 1.2+3.4+...+99.100

Answer 1

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

Answer 2

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: \(\text{1.2+3.4+...+99.100 = 333300}\)

Answer 3

đề sai rùi bạn ơi

phải là tính :1.2+2.3+........+99.100