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
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}`
Giải thích các bước giải:
Đáp án:
Giải thích các bước giải:
a) B = (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
=$\frac{(100 + 1) . 100}{2}$
= 5050
b) C = (2^2 – 1)(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
= (2^8 – 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
= 2^{128} – 1 + 1 = 2^{128}
Cho xin 5 sao được ko ạ!
—–quang148—–