Đáp án:
a, `B = (100^2 - 99^2) +( 98^2 - 97^2) + ... + (2^2 - 1^2)`
`= (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + ... + (2 - 1)(2 + 1)`
`= 1. (100 + 99) + 1.(98 + 97) + ... + 1.(2 + 1)`
`= 1 + 2 + ... + 99 + 100`
`= [(100 + 1).100]/2`
`= 5050`
b, Ta có :
`C = 3(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1) + 1`
Đặt `A = 3(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1)`
`= (2^2 - 1)(2^2 + 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1)`
` = (2^4 - 1)(2^4 + 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1)`
`= (2^8 - 1)(2^8 + 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1)`
`= (2^{16} - 1)(2^{16} + 1)(2^{32} + 1)(2^{64} + 1)`
`= (2^{32} - 1)(2^{32} + 1)(2^{64} + 1)`
`= (2^{64} - 1)(2^{64} + 1)`
`= 2^{128} - 1`
`=> C = 2^{128} - 1 + 1 = 2^{128}`
Giải thích các bước giải:
