HP
1
K
Khách
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DN
1
6 tháng 7 2016
\(S=4\cdot\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(\left(3^2-1\right)S=4\cdot\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(8S=4\cdot\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
\(2S=\left(3^8-1\right)\left(3^8+1\right)\cdot...\cdot\left(3^{64}+1\right)\)
...
\(2S=3^{128}-1\)
Vậy S < 3128 - 1
NT
1
XO
27 tháng 10 2020
Ta có A = (32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = 8(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = (32 - 1)(32 + 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = (34 - 1)(34 + 1)(38 + 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = (38 - 1)(38 + 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = (316 - 1)(316 + 1)(332 + 1)(364 + 1)
=> 8A = (332 - 1)(332 + 1)(364 + 1)
=> 8A = (364 - 1)(364 + 1)
=> 8A = 3128 - 1 (1)
Đặt B = 3126
=> 8B = 3126 . 8 = 3126.(32 - 1) = 3128 - 3126 (2)
Từ (1)(2) => 8A > 8B
=> A > B
LH
3
10 tháng 6 2016
A=4(3^2+1)(3^4+1)(3^8+1)...(3^64+1)
2A=8(3^2+1)(3^4+1)(3^8+1)...(3^64+1)
2A=(3^2-1)(3^2+1)(3^4+1)(3^8+1)...(3^64+1)
2A=(3^4-1)(3^4+1)(3^8+1)...(3^64+1)
2A=(3^8-1)(3^8+1)....(3^64+1)
2A=(3^16-1)...(3^64+1)
......
2A=(3^64-1)(3^64+1)
2A=3^128-1
A=(3^128-1)/2
=> A>B
10 tháng 6 2016
\(A=4\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^2-1\right)\left(3^2+1\right)...\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^8-1\right)\left(3^8+1\right)...\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^{16}-1\right)\left(3^{16}+1\right)...\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^{32}-1\right)\left(3^{32}+1\right)\left(3^{64}+1\right)\)
\(\Leftrightarrow4A=\left(3^{64}-1\right)\left(3^{64}+1\right)\Leftrightarrow4A=3^{128}-1\Leftrightarrow A=\frac{3^{128}-1}{4}\)
Ta có \(\frac{3^{128}-1}{4}< 3^{128}-1\Rightarrow A< B\)
Lâm Huyền:Bạn sai đề rồi B phải là 3128-1 chứ !
DP
1
LT
1
KT
14 tháng 7 2018
\(A=4\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(=\frac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(=\frac{1}{2}\left(3^4-1\right)\left(3^4+1\right)....\left(3^{64}+1\right)\)
\(.........\)
\(=\frac{1}{2}\left(3^{168}-1\right)\)\(< \)\(3^{168}-1\)
\(\Rightarrow\)\(A< B\)
10 tháng 10 2018
\(A=4\left(3^2+1\right)\left(3^4+1\right).....\left(3^{64}+1\right)\)
\(=\frac{1}{2}\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right).....\left(3^{64}+1\right)\)
\(=\frac{1}{2}\left(3^4-1\right)\left(3^4+1\right).....\left(3^{64}+1\right)\)
\(=\frac{1}{2}\left(3^{128}-1\right)< B\)
10 tháng 10 2018
\(A=4\left(3^2+1\right)\left(3^4+1\right)....\left(3^{64}+1\right)\)
\(\Rightarrow2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right).....\left(3^{64}+1\right)\)
\(=\left(3^4-1\right)\left(3^4+1\right).....\left(3^{64}+1\right)=\left(3^{64}-1\right)\left(3^{64}+1\right)=3^{128}-1=B\)
\(\Rightarrow A< B\)
A=4(32+1)(34+1)(38+1)...(364+1)
=>2A=8(32+1)(34+1)(38+1)....(364+1)
=(32-1)(32+1)(34+1)(38+1).....(364+1)
=(34-1)(34+1)(38+1)....(364+1)
=(38-1)(38+1).....(364+1)
tương tự như thế ta được
2A=3128-1
=>A\(\frac{3^{128}-1}{2}\)
=>B>A