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LT
2
LT
1
S
26 tháng 3 2017
\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{624}{625}\)
\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{24.26}{25.25}\)
\(=\frac{1.2.3....24}{2.3.4....25}\cdot\frac{3.4.5....26}{2.3.4....25}\)
\(=\frac{1}{25}\cdot\frac{26}{2}=\frac{26}{50}=\frac{13}{25}\)
\(\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{8}\right)\cdot\left(1+\frac{1}{15}\right)\cdot\cdot\cdot\cdot\left(1+\frac{1}{9999}\right)\)
\(=\frac{4}{3}\cdot\frac{9}{8}\cdot\frac{16}{15}\cdot\cdot\cdot\cdot\frac{10000}{9999}\)
\(=\frac{2.2}{1.3}\cdot\frac{3.3}{2.4}\cdot\frac{4.4}{3.5}\cdot\cdot\cdot\cdot\frac{100.100}{99.101}\)
\(=\frac{2.3.4...100}{1.2.3...99}\cdot\frac{2.3.4...100}{3.4.5...101}\)
\(=\frac{100}{1}\cdot\frac{2}{101}=\frac{200}{101}\)
27 tháng 3 2017
3/4.8/9.15/16.....624/625
=(1.3)/(2.2).(2.4)/(3.3).(3.5)/(4.4)...(24.26)/(25.25)
=(1.2.3....24).(3.4.5....26)/(2.3.4...25).(2.3.4...25)
=26/25.2
=26/50
=13/25
NT
1
16 tháng 3 2020
- Đặt \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{624}{625}\)
- Ta có: \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{624}{625}\)
\(\Leftrightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{24.26}{25.25}\)
\(\Leftrightarrow A=\frac{1.2.3.....24}{2.3.4.....25}.\frac{3.4.5.....26}{2.3.4.....25}\)
\(\Leftrightarrow A=\frac{1}{25}.\frac{26}{2}\)
\(\Leftrightarrow A=\frac{1}{25}.13=\frac{13}{25}\)
Vậy \(A=\frac{13}{25}\)
19 tháng 3 2017
\(\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{624}{625}\)
\(=\dfrac{3.8.15...624}{4.9.16...625}\)
\(=\dfrac{\left(1.3\right)\left(2.4\right)\left(3.5\right)...\left(24.26\right)}{\left(2.2\right)\left(3.3\right)\left(4.4\right)...\left(25.25\right)}\)
\(=\dfrac{\left(1.2.3...24\right)\left(3.4.5...26\right)}{\left(2.3.4...25\right).\left(2.3.4...25\right)}\)
\(=\dfrac{1.26}{25.2}\)
\(=\dfrac{13}{25}\)
BN
19 tháng 3 2017
\(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot\cdot\cdot\dfrac{624}{625}\)
\(=\dfrac{1.3}{2.2}\cdot\dfrac{2.4}{3.3}\cdot\dfrac{3.5}{4.4}\cdot\cdot\cdot\dfrac{24.26}{25.25}\)
\(=\dfrac{1.2.3....24}{2.3.4....25}\cdot\dfrac{3.4.5....26}{2.3.4...25}\)
\(=\dfrac{1}{25}\cdot\dfrac{26}{2}=\dfrac{13}{25}\)
DD
6 tháng 8 2015
375.376=3.125.47.8=141.1000=141000
624.625=16.39.625=10000.39=39000
13.81.215=226395
19 tháng 7 2019
\(F=\frac{3}{4}\cdot\frac{8}{9}\cdot........\cdot\frac{9999}{1000}\)
\(F=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot....\cdot\frac{99.101}{100.100}\)
\(F=\frac{1}{2}.\frac{101}{100}=\frac{101}{200}\)
_Hắc phong_
VC
Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )
CTV
VIP
19 tháng 7 2019
\(\frac{3}{4}.\frac{8}{9}.....\frac{9999}{10000}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.....\frac{99.101}{100.100}\)
\(=\frac{1.2.3.....99}{2.3.4.....100}.\frac{3.4.5.....101}{2.3.4.....100}=\frac{1}{100}.\frac{101}{2}\)
\(=\frac{101}{200}\)
15 tháng 7 2019
\(\frac{9^6\times16^4}{27^4\times8^3}\)
\(=\frac{(3^2)^6\times(2^4)^4}{(3^3)^4\times(2^3)^3}\)
\(=\frac{3^{12}\times2^{16}}{3^{12}\times2^9}\)
\(=\frac{2^{16}}{2^9}\)
\(=2^7\)
\(=128\)
ai trả lời nhanh cho 3 k
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{624}{625}=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{24.26}{25.25}\)
\(\frac{1.2.3.4.....24}{2.3.4.5.....25}.\frac{3.4.5.....26}{2.3.4.5......25}=\frac{1}{25}.\frac{26}{2}=\frac{13}{25}\)