\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)....\left(\frac{1}{999}+1\right)=?\)
Những câu hỏi liên quan
\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{999}-1\right)\)
Tìm tích
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right).....\left(\frac{1}{999}+1\right)\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)....\left(\frac{1}{1000}-1\right)\)
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right)..\left(\frac{1}{999}+1\right)=\frac{3}{2}.\frac{4}{3}....\frac{1000}{999}=\frac{3.4.5...1000}{2.3....999}=\frac{100}{2}=50\)
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b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)...\left(\frac{1}{1000}-1\right)=\left(-\frac{1}{2}\right).\left(\frac{-2}{3}\right)...\left(\frac{-999}{1000}\right)=-\frac{1}{1000}\)
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Tính nhanh :
\(D=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{999}\right).\left(1-\frac{1}{1000}\right)\)
\(D=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)
\(D=\frac{1}{1000}\)( rút gọn những thừa số giống nhau ở tử và mẫu)
Vậy \(D=\frac{1}{1000}\)
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D = \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{999}{1000}\)
D = \(\frac{1}{1000}\)
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\(D=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{999}\right)\left(1-\frac{1}{1000}\right)\)
\(\Rightarrow D=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)
\(\Rightarrow D=\frac{1.2.3.....998.999}{2.3.4.....999.1000}\)
\(\Rightarrow D=\frac{1}{1000}\)
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3. Tính:
a) \(2^3-\left(\frac{1}{3}\right)^0.\sqrt{81}\)
b) \(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{998}-1\right).\left(\frac{1}{999}-1\right)\)
a) 2^3-(1/3)^0.9
=8-(1/3)^0
=8-1
=7
b) mk quên cách giải rồi
sorry mai nha
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Tìm tích:
1.\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times...\times\left(\frac{1}{999}+1\right)\)
2.\(\left(\frac{1}{2}-1\right)\times\left(\frac{1}{3}-1\right)\times\left(\frac{1}{4}-1\right)\times...\times\left(\frac{1}{1000}-1\right)\)
3.\(\frac{3}{2^2}\times\frac{8}{3^2}\times\frac{15}{4^2}\times...\times\frac{99}{10^2}\)
biết làm bài 1 thôi
\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\cdot\cdot\cdot\times\left(\frac{1}{999}+1\right)\)
= \(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdot\cdot\cdot\times\frac{1000}{999}\)
lượt bỏ đi còn :
\(\frac{1000}{2}=500\)
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Tínha)left(frac{1}{2}+1right).left(frac{1}{3}+1right).left(frac{1}{4}+1right)...left(frac{1}{999}+1right); b)left(frac{1}{2}-1right).left(frac{1}{3}-1right).left(frac{1}{4}-1right)...left(frac{1}{1000}-1right)c)frac{3}{2^2}.frac{8}{3^2}.frac{15}{4^2}...frac{99}{10^2}
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Tính
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right);\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)
c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)
lam on ai biet thi chi trong toi nay tui se cho ma ngay mai la phai nop rui
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( 1/2 + 1 ) . ( 1/3 + 1 ) . ( 1/4 + 1 ) . ... . ( 1/999 + 1 )
= 3/2 . 4/3 . 5/4 . ... . 1000/999
= 3 . 4 . 5 . ... . 1000 / 2 . 3 . 4 . ... . 999
= 500
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\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).......\left(\frac{1}{998}-1\right).\left(\frac{1}{999}-1\right)\)
Lời giải:
Ta có:
\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{998}-1\right)\left(\frac{1}{999}-1\right)=\frac{1-2}{2}.\frac{1-3}{3}.....\frac{1-998}{998}.\frac{1-999}{999}\)
\(=\frac{-1}{2}.\frac{-2}{3}.\frac{-3}{4}....\frac{-997}{998}.\frac{-998}{999}\)
\(=\frac{(-1)(-2)(-3)....(-998)}{2.3.4...999}=\frac{1.2.3....998}{2.3.4...999}=\frac{1}{999}\)
Bài 1: frac{1}{6}+frac{-5}{7}: x frac{-7}{18}Bài 2: Tìm tícha)left(frac{1}{2}+1right).left(frac{1}{3}+1right).left(frac{1}{4}+1right)...left(frac{1}{999}+1right)b)left(frac{1}{2}-1right).left(frac{1}{3}-1right).left(frac{1}{4}-1right)...left(frac{1}{1000}-1right)c)frac{3}{2^2}.frac{8}{3^2}.frac{15}{4^2}...frac{99}{10^2}
Đọc tiếp
Bài 1: \(\frac{1}{6}\)+\(\frac{-5}{7}\): x = \(\frac{-7}{18}\)
Bài 2: Tìm tích
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)
c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)
Bài 1: frac{1}{6}+frac{-5}{7}: x frac{-7}{18}
Bài 2: Tìm tích
a)left(frac{1}{2}+1right).left(frac{1}{3}+1right).left(frac{1}{4}+1right)...left(frac{1}{999}+1right)
b)left(frac{1}{2}-1right).left(frac{1}{3}-1right).left(frac{1}{4}-1right)...left(frac{1}{1000}-1right)
c)frac{3}{2^2}.frac{8}{3^2}.frac{15}{4^2}...frac{99}{10^2}
Đọc tiếp
Bài 1: \(\frac{1}{6}\)+\(\frac{-5}{7}\): x = \(\frac{-7}{18}\)
Bài 2: Tìm tích
a)\(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)...\left(\frac{1}{999}+1\right)\)
b)\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right)...\left(\frac{1}{1000}-1\right)\)
c)\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{99}{10^2}\)
Bài 1:
\(\Leftrightarrow-\dfrac{5}{7}:x=-\dfrac{7}{18}-\dfrac{1}{6}=\dfrac{-7}{18}-\dfrac{3}{18}=\dfrac{-10}{18}=\dfrac{-5}{9}\)
=>x=5/9:5/7=7/9
Bài 2:
a: \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{1000}{999}=\dfrac{1000}{2}=500\)
b: \(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-999}{1000}\)
\(=-\dfrac{1}{1000}\)
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