Tính nhanh:
A=(1000-1^3).(1000-2^3)..........(1000-2010^3)
(1000-1^3)(1000-2^3)...(1000-2010^3)
\(=\left(1000-1^3\right)\cdot\left(1000-8\right)\cdot...\cdot\left(1000-1000\right)\cdot...\left(1000-2010^3\right)\)
=0
Chứng minh rằng:
11000+21000+31000+⋯+20101000=0(mod 2011),
Tính nhanh A = (1000-1^3).(1000-2^3).(1000-3^3).................(1000-50^3)
Tính nhanh tổng sau:(1000-1^3).(1000-2^3).(1000-3^3)...........(1000-55^3)
dap an bang 0 ma minh khong biet cach trinh bay
(1000-1^3).(1000-2^3).(1000-3^3)...........(1000-55^3)
=(1000-1^3).(1000-2^3).(1000-3^3).......(1000-10^3)........(1000-55^3)
=(1000-1^3).(1000-2^3).(1000-3^3).......0........(1000-55^3)
=0
tính (1000-1^3).(1000-2^3).(1000-3^3...(1000-50^3)
Tính nhanh
(1000-1^3).(1000-2^3).(1000-3^3). ... .(1000-15^3)
=(1000-1^3).(1000-2^3).(1000-3^3)......(1000-10^3)....(1000-15^3)
=(1000-1^33).(1000-2^3).(1000-33).......0..........(1000-15^3) =0
\(\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-15^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-10^3\right)...\left(1000-15^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)...\cdot0\cdot...\left(1000-15^3\right)\)
\(=0\)
Tính: (1000-1^3)*(1000-2^3)*........*(1000-50^3)
( 1000 - 13 ) . ( 1000 - 23 ) ... ( 1000 - 503 )
= ( 1000 - 13 ) . ( 1000 - 23 ) ... ( 1000 - 103 ) ... ( 1000 - 503 )
= ( 1000 - 13 ) . ( 1000 - 23 ) ... 0 ... ( 1000 - 503 )
= 0
Tính ( 1000 - 13). ( 1000 - 23). ( 1000 - 33)....(1000 - 503)
A=(1+1999/1).(1+1992/2).(1+1999/3)...(1+1999/1000)/(1+1000/1).(1+1000/2).(1+1000/3)...(1+1000/1999)
Tính A