Question

\(A=1.2.3+2.3.4+3.4.5+...+98.99.100\)

Answer 1

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101\

4A=98.99.100.101

A=\(\dfrac{\text{98.99.100.101}}{4}\)

tick nha

Answer 2

Ta có: \(A=1.2.3+2.3.4+3.4.5+...+98.99.100\)

\(4A=\left(1.2.3+2.3.4+...+98.99.100\right)4\)

\(4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)...+98.99.100.\left(101-97\right)\)

\(4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100\)

\(4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+...+97.98.99.100-97.98.99.100+98.99.100.101\)

\(4A=98.99.100.101\)

\(\Rightarrow A=\dfrac{98.99.100.101}{4}=24497550\)

Answer 3

\(A=1.2.3+2.3.4+3.4.5+...+98.99.100\)

\(4A=1.2.3.4+2.3.4.\left(5-1\right)+...+98.99.100.\left(101-97\right)\)\(4A=1.2.3.4+2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.100\)\(4A=98.99.100.101\)

\(A=\dfrac{98.99.100.101}{4}=24497550\)