Tính : `A = 2(3^2 + 1)(3^4 + 1)(3^8 +1)….(3^{64} + 1)` Question Tính : `A = 2(3^2 + 1)(3^4 + 1)(3^8 +1)….(3^{64} + 1)` in progress 0 Môn Toán Acacia 4 years 2020-10-13T20:05:44+00:00 2020-10-13T20:05:44+00:00 2 Answers 101 views 0
Answers ( )
Đáp án:
Giải thích các bước giải:
`A=2(3^2+1)(3^4+1)(3^8+1)…(3^64+1)`
`=>4A=(3+1)(3-1)(3^2+1)(3^4+1)(3^8+1)…(3^64+1)`
`=>4A=(3^2-1)(3^2+1)(3^4+1)(3^8+1)…(3^64+1)`
`=>4A=(3^4-1)(3^4+1)(3^8+1)…(3^64+1)`
`=>4A=(3^8-1)(3^8+1)..(3^64+1)`
`=>4A=(3^16-1)….(3^64+1)`
`=>4A=(3^128-1)`
`=>A=(3^128-1)/4`
Đáp án:
$A = \dfrac{3^{128} -1}{4}$
Giải thích các bước giải:
$A= 2(3^2 + 1)(3^4 + 1)(3^8 +1)\dots(3^{64} + 1)$
$\to A = (3^1 – 1)(3^2 + 1)(3^4 + 1)(3^8 +1)\dots(3^{64} + 1)$
$\to 4A = (3^1 – 1)(3^1 + 1)(3^2 + 1)(3^4 + 1)(3^8 +1)\cdots(3^{64} + 1)$
$\to 4A = (3^2 – 1)(3^2 + 1)(3^4 + 1)(3^8 +1)\dots(3^{64} + 1)$
$\to 4A = (3^4 – 1)(3^4 + 1)(3^8 +1)\dots(3^{64} + 1)$
$\to 4A = (3^8 -1)(3^8 +1)\dots(3^{64} + 1)$
$\to 4A = (3^{64} -1)(3^{64} -1)$
$\to 4A = 3^{128} -1$
$\to A = \dfrac{3^{128} -1}{4}$