Question

Tính A=1.2+2.3+3.4+.....+100.101

Answer 1

Ta có: \(A=1.2+2.3+3.4+...+100.101\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...+100.101.3\)

\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+100.101\left(102-99\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+100.101.102-99.100.101\)

\(\Rightarrow3A=\left(1.2.3-1.2.3\right)+...+\left(99.100.101-99.100.101\right)+100.101.102\)

\(\Rightarrow3A=\) \(100.101.102\)

\(\Rightarrow A=\dfrac{100.101.102}{3}=343400\)

Vậy \(A=343400.\)

Answer 2

A = 1.2+2.3+3.4+.....+100.101

3A = 1.2.3+2.3.4+3.4.3+...........+99.100.3

3A= 1.2.(3-0)+ 2.3.(4-1)+ 3.4.(5-2)....... . 99.100.(101-98)

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

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A = 999900

=> A = 999900 : 3

=> A = 333300

Answer 3

câu này trên gg có r` bn!! bn lên tra nhé! mk k lm lại nx! Tiến Đạt

ps: gg là google