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ND
0
PN
0
13 tháng 2 2018
\(B=2016.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2014.2016}\right)\)
= \(2016.\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}....\frac{2015^2}{2014.2016}\)
= \(2016.\frac{2.3.4....2015}{1.2.3.4.5...2014.2015.2016}.\frac{2.3.4....2015}{3.4.5...2014}\)
= \(2016.\frac{1}{2016}.2.2015=2.2015=4030\)
TN
1
6 tháng 4 2022
\(C=\left(1+\frac{1}{1.3}\right)\)\(.\left(1+\frac{1}{2.4}\right)\)\(.\left(1+\frac{1}{3.5}\right)\)\(.\left(1+\frac{1}{2014.2016}\right)\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{2015^2}{2014.2016}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{2015.2015}{2014.2016}\)
\(=\frac{\left(2.3.4...2015\right).\left(2.3.4...2015\right)}{\left(1.2.3...2014\right).\left(3.4.5...2016\right)}\)
\(=\frac{2015.2}{2016}\)
\(=...\)(tự tinhs)
DD
0
OY
24 tháng 7 2021
A=\(\dfrac{3}{4}.\dfrac{8}{9}.....\dfrac{9999}{10000}\)
A=\(\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.....\dfrac{99.101}{100.100}\)
A=\(\dfrac{1.2.3.....99}{2.3.4.....100}.\dfrac{3.4.....101}{2.3.4.....100}\)
A=\(\dfrac{1}{100}.\dfrac{101}{2}\)
A=\(\dfrac{101}{200}\)
24 tháng 7 2021
\(A=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{99.101}{100.100}\\ =\dfrac{1}{2}.\dfrac{101}{100}=\dfrac{101}{200}\)
\(B=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)...\left(1-\dfrac{1}{10000}\right)\\ =\dfrac{3}{4}.\dfrac{8}{9}...\dfrac{9999}{10000}\)
(làm như câu a)
\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right)....\left(1+\frac{1}{2014.2015}\right)\)
\(\left(1.3+\frac{1}{1.3}\right)...\left(2014.2015+\frac{1}{2014.2015}\right)\)
\(\left(\frac{2.2}{1.3}\right)...\left(\frac{2015.2015}{2014.2015}\right)\)
\(\frac{\left(2...2015\right).\left(2...2015\right)}{\left(1.2....2014\right).\left(3...2015\right)}\)
\(\frac{2015.2}{2015}=\frac{2015.2}{1007,5.2}=\frac{2015}{1007.5}=2\)
đúng 100%
\(C=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)..........\left(1+\frac{1}{2014.2016}\right)\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}..........\frac{2015^2}{2014.2016}\)
\(=\frac{2^2.3^2............2015^2}{\left(1.3\right)\left(2.4\right).......\left(2014.2016\right)}\)
\(=\frac{\left(2.3......2015\right)\left(2.3.......2015\right)}{\left(1.2.....2014\right)\left(3.4.......2016\right)}\)
\(=\frac{2.2015}{1.2016}=\frac{2015}{1008}\)