\(\left(1-\frac{2}{2\times3}\right)\left(1-\frac{2}{3\times4}\right)\left(1-\frac{2}{4\times5}\right)...\left(1-\frac{2}{99\times100}\right)\)= ?
Những câu hỏi liên quan
Tính:\(\left(1-\frac{2}{2\times3}\right)\left(1-\frac{2}{3\times4}\right)\left(1-\frac{2}{4\times5}\right)....\left(1-\frac{2}{99\times100}\right)\)
a,A=\(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)
b,B=\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{998\times999\times100}\)
c,C=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1\times98+2\times97+3\times96+...+98\times1}\)
Tính nhanh:\(\frac{\left(1+2\right)\times3}{\left(2+3\right)\times4}+\frac{\left(2+3\right)\times4}{\left(3+4\right)\times5}+...+\frac{\left(999+1000\right)\times1001}{\left(1000+1001\right)\times1002}+\frac{\left(1000+1001\right)\times1002}{\left(1001+1002\right)\times1003}\)
Tinh \(\left(1-\frac{2}{2\times3}\right)\times\left(1-\frac{2}{3\times4}\right)\times\left(1-\frac{2}{4\times5}\right)\times...\times\left(1-\frac{2}{2015\times2016}\right)\)
tính các tích sauafrac{3}{4}timesfrac{8}{9}timesfrac{15}{16}times...timesfrac{9999}{10000}bleft(1-frac{1}{4}right)timesleft(1-frac{1}{9}right)times...timesleft(1-frac{1}{10000}right)cleft(1-frac{1}{2}right)timesleft(1-frac{1}{3}right)times...timesleft(1-frac{1}{1994}right)dleft(1+frac{1}{1times3}right)timesleft(1+frac{1}{2times4}right)timesleft(1+frac{1}{3times5}right)times...timesleft(1+frac{1}{99times100}right)
Đọc tiếp
tính các tích sau
\(a=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{9999}{10000}\)
\(b=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times...\times\left(1-\frac{1}{10000}\right)\)
\(c=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(d=\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{99\times100}\right)\)
\(d=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{3}.\frac{9}{2.4}.............\frac{10000}{99.101}\)
\(=\frac{2.2}{3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}............\frac{100.100}{99.101}\)
\(=\frac{2.3.4..........100}{2.3.4............99}.\frac{2.3.4...........100}{3.4...........101}\)
\(=100.\frac{2}{101}\)\(=\frac{200}{101}\)
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\(C=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{1993}{1994}\)
\(=\frac{1\times2\times3\times...\times1993}{2\times3\times4\times...\times1994}\)
\(=\frac{1}{1994}\) (Giản ước còn lại như này)
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tính \(A=\frac{1}{2}\times\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{2015\times2017}\right)\)
\(A=\frac{1}{2}\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)...\left(1+\frac{1}{2015\cdot2017}\right)\)\(A=\frac{1}{2}\left(\frac{1\cdot3+1}{1\cdot3}\right)\left(\frac{2\cdot4+1}{2\cdot4}\right)...\left(\frac{2015\cdot2017+1}{2015\cdot2017}\right)\)
\(A=\frac{1^2}{2}\cdot\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\cdot\cdot\frac{2016^2}{2015\cdot2017}\)
\(A=\frac{1^2\cdot2^2\cdot3^2\cdot\cdot\cdot2016^2}{2\cdot1\cdot3\cdot2\cdot4\cdot\cdot\cdot2015\cdot2017}\)
\(A=\frac{2016}{2017}\)
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=\(\left(1+\frac{1}{1\times3}\right)\left(1+\frac{1}{2\times4}\right)\left(1+\frac{1}{3\times5}\right)...\left(1+\frac{1}{2016\times2018}\right)\)
Ai giúp với
= 1.3+1/1.3 . 2.4+1/2.4 . ....... . 2016.2018+1/2016.2018
= 2^2/1.3 . 3^2/2.4 . ....... . 2017^2/2016.2018
= 2.3. ...... . 2017/1.2. ..... . 2016 . 2.3. ..... . 2017/3.4. ...... . 2018
= 2017 . 2/2018
= 2017/1009
Tk mk nha
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Tính luôn :
= 4/3 . 9/8 . 16/15 .. . 4068289/2016 . 2018
= 4/3 . 9/8 . 16/15 . .. 2017 x 2017 / 2016. 2018
= 4 . 9 . 16 ... 2017 . 2017 / 3 . 8 . 15 . ...2016 . 2018
= 2 . 2 . 3 . 3 . 4 . 4 ... 2017 . 2017 / 3 . 2 . 4 . 3 . 5 ...2016 . 2018
= ( 2 . 3 . 4 ... 2017 ) . ( 2 . 3 . 4 ... 2017 ) / ( 3 . 4 . 5 ... 2016 ) . ( 2 . 3 . 4 . 5 ...2018 )
= 2 . 2017 / 2018
= 2017 / 1009
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Xem thêm câu trả lời
\(A=\left[1-\left(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+......+\frac{1}{98\times99\times100}\right)\right]\times\frac{14851}{19800}\)
CMR với mọi số tự nhiên n lớn hơn hoặc bằng 1 thì:
\(\left(1+\frac{1}{1\times3}\right)\left(1+\frac{1}{2\times4}\right)\left(1+\frac{1}{3\times5}\right).......\left(1+\frac{1}{n\times\left(n+2\right)}\right)< 2\)