Question

cho A= 1.2 + 2.3 + 3.4 + 4.5 + .......+ 99.100

Hãy tính tổng A (ahihi)

Answer 1

\(A=1\cdot2+2\cdot3+3\cdot4+4\cdot5+...+99\cdot100\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+99\cdot100\cdot3\)

\(3A=1\cdot2\cdot\left(3-0\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+99\cdot100\cdot\left(101-98\right)\)

\(3A=1\cdot2\cdot3-0+2\cdot3\cdot4-1\cdot2\cdot3+3\cdot4\cdot5-2\cdot3\cdot4+...99\cdot100\cdot101-98\cdot99\cdot100\)

\(3A=98\cdot99\cdot100\Rightarrow A=\frac{98\cdot99\cdot100}{3}=...\)