Question

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

các bạn giúp mình nhé :=)

Answer 1

\(A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 100 . 101\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+100\cdot101\cdot\left(102-99\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+100\cdot101\cdot102-99\cdot100\cdot101\)

\(3A=100\cdot101\cdot102\)

\(3A=1030200\)

\(A=1030200\text{ : }3\)

\(A=343400\)

Answer 2

\(A = 1 . 2 + 2 . 3 + 3 . 4 + ... + 100 . 101\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+...+100\cdot101\cdot\left(102-99\right)\)

\(3A=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+100\cdot101\cdot102-99\cdot100\cdot101\)

\(3A=100\cdot101\cdot102\)

\(3A=1030200\)

\(A=1030200\text{ : }3\)

\(A=343400\)