`a)`
Ta có :
`A = 1999 . 2001 = (2000 - 1)(2000+1) = 2000^2 - 1 < 2000^2`
Mà `B = 2000^2`
`=> B > A`
`b)`
Ta có :
`B = (2+1)(2^2+1)(2^4+1)(2^8+1)`
`=> (2-1) . B= (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)`
`=> B = (2^2-1)(2^2+1)(2^4+1)(2^8+1)`
`=> B = (2^4 - 1)(2^4+1)(2^8+1)`
`=> B = (2^8-1)(2^8+1)`
`=> B = 2^16 - 1 < 2^16`
Mà `A = 2^16`
`=> B < A`
`c)`
Ta có :
`A = 2011 . 2013 = (2012 -1)(2012+1)=2012^2 -1 < 2012^2`
Mà `B = 2012^2`
`=> A< B`
`d)`
Ta có :
`A = 4(3^2+1)(3^4+1)...(3^64+1)`
`=> (3^2-1) . A = 4 .(3^2-1) (3^2+1)(3^4+1)...(3^64+1)`
`=> 8A = 4 (3^4 -1)(3^4+1)...(3^64+1)`
`=> 2A = (3^4 - 1)(3^4+1)..(3^64+1)`
`=> 2A = (3^8-1)(3^8+1)....(3^64+1)`
`=> 2A = (3^16-1)(3^16 + 1)...(3^64+1)`
`=> 2A = (3^32-1)(3^32+1)(3^64+1)`
`=> 2A = (3^64-1)(3^64+1)`
`=> 2A = 3^128 - 1`
Mà `B = 3^128-1`
`=> 2A = B`
`=> A < B`
