tính nhanh
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)
K
Khách
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B
4
TT
1
11 tháng 10 2016
A = (2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264
A = (2 - 1)(2 + 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264
A = (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264
A = (24 - 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1) - 264
A = (28 - 1)(28 + 1)(216 + 1)(232 + 1) - 264
A = (216 - 1)(216 + 1)(232 + 1) - 264
A = (232 - 1)(232 + 1) - 264
A = 264 - 1 - 264
A = -1
ND
Nguyễn Đức Trí
VIP
10 tháng 8 2023
7) \(A=1^2-2^2+3^2-4^2+...-2004^2+2005^2\)
\(A=\left(-1\right)\left(1^{ }+2\right)+\left(-1\right)\left(3+4\right)+...+\left(-1\right)\left(2003+2004\right)+2005^2\)
\(A=-\left(1+2+3+...+2004\right)+2005^2\)
\(A=-\dfrac{2004.\left(2004+1\right)}{2}+2005^2\)
\(A=-1002.2005+2005^2\)
\(A=2005\left(2005-1002\right)=2005.1003=2011015\)
ND
Nguyễn Đức Trí
VIP
10 tháng 8 2023
8) \(B=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\dfrac{\left(2^2-1\right)}{2-1}\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)
\(B=\left(2^{64}-1\right)-2^{64}\)
\(B=-1\)
13 tháng 2 2022
\(\dfrac{3}{-4}+\dfrac{-3}{-4}+\dfrac{2}{5}+\dfrac{-1}{2}+\dfrac{3}{5}\\ =\left(\dfrac{-3}{4}+\dfrac{3}{4}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{1}{2}\\ =0+1-\dfrac{1}{2}\\ =1-\dfrac{1}{2}\\ =\dfrac{1}{2}\)
13 tháng 2 2022
\(=\left(-\dfrac{3}{4}+\dfrac{3}{4}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{1}{2}=1-\dfrac{1}{2}=\dfrac{1}{2}\)
MT
0
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(\Leftrightarrow2^{64}-1\)