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DN
0
TH
0
22 tháng 2 2017
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.....1\frac{1}{99}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}......\frac{100}{99}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.....\frac{10.10}{9.11}\)
\(=\frac{\left(2.3.4...10\right)\left(2.3.4....10\right)}{\left(1.2.3...9\right)\left(3.4.5....11\right)}\)
\(=\frac{10.2}{11}=\frac{20}{11}\)
23 tháng 6 2015
B=3/2x4/3x...........x2018/2017
=3x4x5x...........x2018/2x3x2x2x............x2017
=2x2018
=4036
A,C tương tự
6 tháng 11 2021
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot\dfrac{25}{24}\cdot\dfrac{36}{35}=\dfrac{12}{7}\)
9 tháng 12 2022
= 4/3*9/8*16/15*25/24*36/35
=2*2/1*3 * 3*3/2*4 *4*4/3*5 *5*5/4*6 * 6*6/5*7
= (2*3*4*5*6 / 1*2*3*4*5) * ( 2*3*4*5*6 / 3*4*5*6*7)
=6/1* 2/7
= 12/7
GD
2
11 tháng 8 2016
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{100}{99}\)
SN
11 tháng 8 2016
\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times1\frac{1}{24}\times...\times1\frac{1}{99}\)
\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times\frac{25}{24}\times...\times\frac{100}{99}\)
\(=\frac{2\times2}{1\times3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times\frac{5\times5}{4\times6}\times...\times\frac{10\times10}{9\times11}\)
\(=\frac{2}{1}\times\frac{10}{11}\)
\(=\frac{20}{11}\)
A = 1\(\dfrac{1}{3}\) x 1\(\dfrac{1}{8}\) x 1\(\dfrac{1}{15}\) x 1\(\dfrac{1}{24}\) x ... x 1\(\dfrac{1}{99}\)
A = \(\dfrac{4}{3}\) x \(\dfrac{9}{8}\) x \(\dfrac{16}{15}\) x \(\dfrac{25}{24}\) x ... x \(\dfrac{100}{99}\)
A = \(\dfrac{2\times2}{1\times3}\) x \(\dfrac{3\times3}{2\times4}\) x \(\dfrac{4\times4}{3\times5}\) x \(\dfrac{5\times5}{4\times6}\) x ... x \(\dfrac{10\times10}{9\times11}\)
A = \(\dfrac{\left(2\times3\times...\times9\times10\right)\times\left(2\times3\times4\times...\times10\right)}{\left(1\times2\times3\times..\times9\right)\times\left(3\times4\times..\times10\times11\right)}\)
A = (\(\dfrac{2\times3\times..\times9}{2\times3\times..\times9}\times\dfrac{10}{1}\)) x (\(\dfrac{3\times4\times...\times9\times10}{3\times4\times...\times9\times10}\) \(\times\)\(\dfrac{2}{11}\) )
A = \(\dfrac{10}{1}\) \(\times\) \(\dfrac{2}{11}\)
A = \(\dfrac{20}{11}\)
\(1\dfrac{1}{3}\cdot1\dfrac{1}{8}\cdot...\cdot1\dfrac{1}{99}\)
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot...\cdot\dfrac{100}{99}\)
\(=\dfrac{2\cdot3\cdot...\cdot10}{1\cdot2\cdot...\cdot9}\cdot\dfrac{2\cdot3\cdot...\cdot10}{3\cdot4\cdot...\cdot11}\)
\(=\dfrac{10}{1}\cdot\dfrac{2}{11}=\dfrac{20}{11}\)