\(A=\left(1000-1^3\right)\left(1000-2^3\right)......\left(1000-25^3\right)\)
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\(\left(1000-1^{ }3\right).\left(1000-2^{ }3\right).\left(1000-3^{ }3\right)....\left(1000-25^{ }3\right)\)
\(^{\left(-1\right)^2.\left(-1\right)^{ }3.\left(-1\right)^{ }4.......\left(-1\right)^{ }100}\)
ai trả lời nhanh nhất mk sẽ k cho 3 lần
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Giúp mik vớiTính nhanh:a. Aleft(-1right)^{2n}.left(-1right)^n.left(-1right)^{n+1}left(nin Nright)b. Bleft(10000-1^2right)left(10000-2^2right)left(10000-3^2right)..left(10000-1000^2right)c. Cleft(frac{1}{125}-frac{1}{1^3}right)left(frac{1}{125}-frac{1}{2^3}right)left(frac{1}{125}-frac{1}{3^3}right)...left(frac{1}{125}-frac{1}{25^3}right)d. D1999^{left(1000-1^3right)left(1000-2^3right)left(1000-3^3right)...left(1000-10^3right)}
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Giúp mik với
Tính nhanh:
a. A=\(\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}\left(n\in N\right)\)
b. B=\(\left(10000-1^2\right)\left(10000-2^2\right)\left(10000-3^2\right)..\left(10000-1000^2\right)\)
c. C=\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)\left(\frac{1}{125}-\frac{1}{3^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
d. D=\(1999^{\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-10^3\right)}\)
a) \(A=\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}=\left(-1\right)^{3n+1}\)
b) \(B=\left(10000-1^2\right)\left(10000-2^2\right).........\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right)......\left(10000-100^2\right)....\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right).....\left(10000-10000\right).....\left(10000-1000^2\right)=0\)
c) \(C=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)..........\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right).....\left(\frac{1}{125}-\frac{1}{5^3}\right)......\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)........\left(\frac{1}{125}-\frac{1}{125}\right).....\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
d) \(D=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-10^3\right)}\)
\(=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-1000\right)}=1999^0=1\)
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
Số nào nhân với 0 cũng bằng 0
Vậy A = 0
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\(A=\frac{\left(1+\frac{1999}{1}\right)\left(1+\frac{1999}{2}\right)\left(1+\frac{1999}{3}\right)...\left(1+\frac{1999}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)\left(1+\frac{1000}{3}\right)...\left(1+\frac{1000}{1999}\right)}\)
hỏi a = ?
\(Tính:\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right)...\left(1000-50^3\right)\)
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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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: \(\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right)......\left(1000-50^3\right)=..........\)
Vì trong dãy trên sẽ có 1000-10\(^3\)=0
\(\Rightarrow\)(1000-1)(1000-2\(^3\))...(1000-50\(^3\))=0
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Tính:
Ta có : 1000 - 13 = 1000 - 1000 = 0
Nên : (= 0
Vậy ...
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Ta có: (1000 - 1^3) . (1000 - 2^3) . (1000 - 3^3) . ... . (1000 - 10^3) . ... . (1000 - 50^3)
= (1000 - 1^3) . (1000 - 2^3) . (1000 - 3^3) . ... . (1000 - 1000). ... . (1000 - 50^3)
= (1000 - 1^3) . (1000 - 2^3) . (1000 - 3^3) . ... . 0 . ... . (1000 - 50^3)
= 0
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Xem thêm câu trả lời
23 tháng 2 2017 lúc 10:31
Tính : \(\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right).....\left(1000-50^3\right)=?\)
\(\left(1000-1^3\right).\left(1000-2^3\right).\left(1000-3^3\right)....\left(1000-50^3\right)\)
\(=\left(1000-1^3\right).\left(1000-2^3\right)...\left(1000-10^3\right)....\left(1000-50^3\right)\)
\(=\left(1000-1^3\right).\left(1000-2^3\right)...\left(1000-1000\right)....\left(1000-50^3\right)\)
\(=\left(1000-1^3\right).\left(1000-2^3\right)...0...\left(1000-50^3\right)\)
\(=0\)
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