Toán Lớp 6: 2^n -1-2-2^2-2^3-……..-2^100=1
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Toán Lớp 6: 2^n -1-2-2^2-2^3-……..-2^100=1
mik cần gấp.giúp mik với
Comments ( 2 )
$ 2^n – 1 – 2 – 2^2 – 2^3 – … – 2^{100} = 1 $
$ ⇒ 2^n – ( 1 + 2 + 2^2 + .. + 2^{100} ) = 1 $
$ A = 1 + 2 + 2^2 + .. + 2^{100} $
$ 2A = 2 + 2^2 + 2^3 + … + 2^{101} $
$ 2A – A = ( 2 + 2^2 + 2^3 + … + 2^{101} ) – ( 1 + 2 + 2^2 + .. + 2^{100} ) $
$ A = 2^{101} – 1 $
$ ⇒ 2^n – ( 1 + 2 + 2^2 + .. + 2^{100} ) = 1 = 2^n – ( 2^{101}-1 ) $
$ 2^n = 2^{101} – 1 + 1 = 2^{101} ⇒ n = 101 $
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