Tính nhanh :
a) \(\frac{2015\cdot2017-1}{2014+2015\cdot2016}\)
b) \(\frac{1}{1\cdot5}+\frac{1}{5\cdot9}+...+\frac{1}{2011\cdot2015}\)
c)\(\frac{12}{35}+\frac{1212}{3535}+\frac{121212}{353535}+\frac{12121212}{35353535}\)
Những câu hỏi liên quan
\(\frac{45\cdot16-17}{45\cdot15+28}\) các bạn đề là tính nhanh nhé
Ví dụ: \(\frac{2016\cdot2015-5}{2014\cdot2016+2011}=\frac{2016\cdot\left(2014+1\right)-5}{2014\cdot2016+2011}=\frac{2016\cdot2014+2016\cdot1-5}{2014\cdot2016-2011}=\frac{2016\cdot2014+2011}{2014\cdot2016+2011}=1\)
Tính nhanh:
\(A=\frac{12}{1\cdot3}+\frac{12}{3\cdot5}+...+\frac{12}{2015\cdot2017}\)
A = 6.(1/1.3+1/3.5+...+1/2015.2017)
= 6.(1/1-1/3+1/3-1/5+...+1/2015-1/2017)
= 6.(1/1-1/2017)
= 6.2016/2017
=12096/2017
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chứng minh :
\(\frac{4}{3\cdot5}-\frac{6}{5\cdot7}+\frac{8}{7\cdot9}-\frac{10}{9\cdot11}+.......+\frac{2016}{2015\cdot2017}>\frac{1}{6}\)
các bạn giúp nhanh mình cái muộn rồi
chứng minh :
\(\frac{4}{3\cdot5}-\frac{6}{5\cdot7}+\frac{8}{7\cdot9}-\frac{10}{9\cdot11}+.......+\frac{2016}{2015\cdot2017}>\frac{1}{6}\)
các bạn giúp nhanh mình cái muộn rồi
\(\frac{4}{3.5}-\frac{6}{5.7}+\frac{8}{7.9}+\frac{10}{9.11}+...+\frac{2016}{2015.2017}\)
\(=2.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=2.\left(\frac{1}{3}-\frac{1}{2017}\right)\)
\(=2.\frac{2014}{6051}\)
\(=\frac{4028}{6051}\)
\(\Rightarrow BT>\frac{1}{6}\)
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TÍNH : \(\frac{1\cdot2016+2\cdot2015+...+2015\cdot2+2016\cdot1}{1\cdot2+2\cdot3+...+2016\cdot2017}\)
so sánh A và B
A= \(\frac{2015\cdot2016-1}{2015\cdot2016}\) B= \(\frac{2016\cdot2017-1}{2016\cdot2017}\)
A = \(\frac{2015.2016-1}{2015.2016}\)= \(\frac{2015.2016}{2015.2016}\)\(-\)\(\frac{1}{2015.2016}\)= 1 \(-\)\(\frac{1}{2015.2016}\)
B = \(\frac{2016.2017-1}{2016.2017}\)= \(\frac{2016.2017}{2016.2017}\)\(-\)\(\frac{1}{2016.2017}\)= 1 \(-\)\(\frac{1}{2016.2017}\)
Vì \(\frac{1}{2015.2016}\)> \(\frac{1}{2016.2017}\)
=> 1 \(-\)\(\frac{1}{2015.2016}\)< \(1-\)\(\frac{1}{2016.2017}\)
=> A < B
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\(\left(2013\cdot2014+2014\cdot2015+2015\cdot2016\right)\cdot\left(1+\frac{1}{3}-1\frac{1}{3}\right)\)
\(\left(2013.2014+2014.2015+2015.2016\right)\left(1+\frac{1}{3}-1\frac{1}{3}\right)\)
\(=\left(2013.2014+2014.2015+2015.2016\right)\left(\frac{4}{3}-\frac{4}{3}\right)\)
\(=\left(2013.2014+2014.2015+2015.2016\right).0\)
\(=0\)
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Xem thêm câu trả lời
Tính B=\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot...\cdot\frac{2015^2}{2014\cdot2016}\)
\(B=\frac{2.2}{1.3}.\frac{3.3}{2.4}...\frac{2015.2015}{2014.2016}\)
\(B=\frac{2.3...2015}{1.2...2014}.\frac{2.3...2015}{3.4...2016}\)
\(B=2015.\frac{1}{1008}\)
\(B=\frac{2015}{1008}\)
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Tính tổng : a) frac{1}{3cdot5cdot7}+frac{1}{5cdot7cdot9}+frac{1}{7cdot9cdot11}+...+frac{1}{2013cdot2015cdot2017} b) left(1-frac{1}{2^2}right)cdotleft(1-frac{1}{3^2}right)cdotleft(1-frac{1}{4^2}right)cdot...cdotleft(1-frac{1}{2017^2}right) c) left(1-frac{1}{1+2}right)cdotleft(1-frac{1}{1+2+3}right)cdot...cdotleft(1-frac{1}{1+2+3+...+2017}right)
Đọc tiếp
Tính tổng :
a) \(\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}+\frac{1}{7\cdot9\cdot11}+...+\frac{1}{2013\cdot2015\cdot2017}\)
b) \(\left(1-\frac{1}{2^2}\right)\cdot\left(1-\frac{1}{3^2}\right)\cdot\left(1-\frac{1}{4^2}\right)\cdot...\cdot\left(1-\frac{1}{2017^2}\right)\)
c) \(\left(1-\frac{1}{1+2}\right)\cdot\left(1-\frac{1}{1+2+3}\right)\cdot...\cdot\left(1-\frac{1}{1+2+3+...+2017}\right)\)