Rút gọn biểu thức: a) B=100^2-99^2=98^2-97^2=..=2^2-1^2 b)C=3(2^2+1)(2^4+1)..(2^64+1)+1 mn giúp em vs mai hok r

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}`

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