Tính : \(\left(1+i\right)^{1000}\)
Những câu hỏi liên quan
1.Tính C=\(\frac{\left(1+\frac{1999}{1}\right)\left(1+\frac{1999}{2}\right)\left(1+\frac{1999}{3}\right)...\left(1+\frac{1999}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)\left(1+\frac{1000}{3}\right)...\left(1+\frac{1000}{1999}\right)}\)
\(C=\frac{\left(1+\frac{1999}{1}\right)\left(1+\frac{1999}{2}\right)...\left(1+\frac{1999}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{1999}\right)}\)=> \(C=\frac{\frac{2000.2001.2002....2999}{1.2.3...1000}}{\frac{1001.1002.1003....2999}{1.2.3...1999}}\)
=> \(C=\frac{\frac{2000.2001.2002....2999}{1.2.3...1000}}{\frac{\left(1001.1002.1003....1999\right).\left(2000.2001.2002...2999\right)}{\left(1.2.3...1000\right).\left(1001.1002...1999\right)}}\)
=> \(C=\frac{2000.2001.2002....2999}{1.2.3...1000}.\frac{\left(1.2.3...1000\right).\left(1001.1002...1999\right)}{\left(1001.1002.1003....1999\right).\left(2000.2001.2002...2999\right)}=1\)
Đáp số: C=1
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Xem thêm câu trả lời
tính G=\(\frac{\left(1+\frac{1015}{1}\right)\left(1+\frac{1015}{2}\right)\left(1+\frac{1015}{3}\right)...\left(1+\frac{1015}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)\left(1+\frac{1000}{3}\right)...\left(1+\frac{1000}{1015}\right)}\)
Tính \(A=\frac{\left(1+\frac{1999}{1}\right)\left(1+\frac{1999}{2}\right)....\left(1+\frac{1999}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)....\left(1+\frac{1000}{1999}\right)}\)
\(A=\frac{\frac{2000\cdot2001\cdot2002\cdot...\cdot2999}{1\cdot2\cdot3\cdot...\cdot1000}}{\frac{1001\cdot1002\cdot1003\cdot...\cdot2999}{1\cdot2\cdot3\cdot...\cdot1999}}=\frac{2000\cdot2001\cdot2002\cdot...\cdot2999}{1\cdot2\cdot3\cdot...\cdot1000}\times\frac{1\cdot2\cdot3\cdot...\cdot1999}{1001\cdot1002\cdot1003\cdot...\cdot2999}\)
\(A=1\)
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\(Tính:\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right)...\left(1000-50^3\right)\)
Tính biểu thức:
\(A=\left(1-\frac{1}{1000}\right).\left(1-\frac{2}{1000}\right).\left(1-\frac{3}{1000}\right).....\left(1-\frac{50000^{1000}}{1000}\right)\)
Tính :
C= \(\frac{\left(1+\frac{1999}{1}\right)\left(1+\frac{1999}{2}\right)...\left(1+\frac{1999}{1000}\right)}{\left(1+\frac{1000}{2}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{1999}\right)}\)
Tính :
\(A=\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right).........\left(1000-50^3\right)\)
Vì 103 = 1000 nên :
( 1000 - 103 ) = 0
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Vậy A = 0
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TÍNH
\(\left(1000-1^3\right)\cdot\left(1000-2^3\right)\cdot\left(1000-3^3\right)\cdot\cdot\cdot\left(1000-50^3\right)\)
Trong biểu thức trên có chứa (1000-103), mà (1000-103)=1000-1000=0
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\(\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-10^3\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-1000\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\cdot0\cdot\left(1000-50^3\right)\)
\(=0\)
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\(\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-10^3\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)...0...\left(1000-50^3\right)\)
\(=0\)
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Tính giá trị biểu thức
\(A=2015^{\left(1000-1^3\right).\left(1000-2^3\right)....\left(1000-20^3\right)}\)