Question

1 x 2 x 3 + 2 x 3 x 4 + ..... + 98 x 99 x 100

Answer 1

Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + ... + 98 . 99 . 100

\(\Rightarrow\) 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . (5 - 1) +...+ 98 . 99 . 100 . (101 - 97)

\(\Rightarrow\) 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 5 - 2 . 3 . 4 . 1 + ... + 98 . 99 . 100 . 101 - 98 . 99 . 100 . 97

\(\Rightarrow\) 4A = 98 . 99 . 100 . 101

\(\Rightarrow\) 4A = 97990200

\(\Rightarrow\) A = 24497550

Answer 2

Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + ... + 98 . 99 . 100

=>4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . (5 - 1) +...+ 98 . 99 . 100 . (101 - 97)

=>4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 5 - 2 . 3 . 4 . 1 + ... + 98 . 99 . 100 . 101 - 98 . 99 . 100 . 97

=>4A = 98 . 99 . 100 . 101 4A = 97990200

=>A = 24497550

Vậy A= 24497550