Tính nhanh

24/25 x 35/36 × 48/49×63/64×.....×399/400

Đặt `A=24/25*35/36*48/49*..............*399/400`

`A=(5^2-1)/5^2*(6^2-1)/6^2*......*(20^2-1)/20^2`

Ta có `a^2-1=(a-1)(a+1)`

`=>5^2-1=4*6;6^2-1=5*7..............,20^20-1=19*21`

`=>A=(4*6)/5^2*(5*7)/6^2*..........*(19*21)/20^2`

`=>A=[(4*5*6*.......*19)*(6*7*8*.........*21)]/[(5*6*7*..............*20)(5*6*7*.........*20)]`

`=>A=4/20*21/5`

`=>A=1/5*21/5=21/25`

Vậy `A=21/25`