Tính:1 1/3 x 1 1/8 x 1 1/15 x 1 1/24 x...x 1 1/99
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
PL
1
26 tháng 3 2017
1/3x1/8x...x1/99
=1/(1x3)x1/(2x4)x...x1/(9x11)
=1/(1x3x2x4x...x9x11)
=1/(1x2x3x3x4x4x5x5x...x9x9x10x11)
26 tháng 3 2017
=1/(1x3)x1/(2x4)x...x1/(9x11)
=1/(1x3x2x4x...x9x11)
=1/(1x2x3x3x4x4x5x5x...x9x10x11)
DN
0
TH
0
21 tháng 10 2023
\(K=\left(1-\dfrac{3}{2\cdot4}\right)\left(1-\dfrac{3}{3\cdot5}\right)\cdot...\cdot\left(1-\dfrac{3}{19\cdot21}\right)\)
\(=\dfrac{3^2-1-3}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{4^2-1-3}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{20^2-4}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{\left(3-2\right)\left(3+2\right)}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{\left(4-2\right)\left(4+2\right)}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{18\cdot22}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{1\cdot5}{2\cdot4}\cdot\dfrac{2\cdot6}{3\cdot5}\cdot...\cdot\dfrac{18\cdot22}{19\cdot21}\)
\(=\dfrac{1\cdot2\cdot3\cdot...\cdot21\cdot22}{2\cdot3\cdot4\cdot5\cdot...\cdot19\cdot20\cdot21}=1\cdot22=22\)
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
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 = \(\dfrac{20}{11}\)
\(1\dfrac{1}{3}\cdot1\dfrac{1}{8}\cdot...\cdot1\dfrac{1}{99}\)
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot...\cdot\dfrac{100}{99}\)
\(=\dfrac{2\cdot3\cdot...\cdot10}{1\cdot2\cdot...\cdot9}\cdot\dfrac{2\cdot3\cdot...\cdot10}{3\cdot4\cdot...\cdot11}\)
\(=\dfrac{10}{1}\cdot\dfrac{2}{11}=\dfrac{20}{11}\)