tính S = ( 1+1/2).(1+1/2+1/3).(1+1/2+1/3+1/4)......(1+1/2+1/3+1/4+...+1/10) chính xác đến 4 chữ số thập phân
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Bài 1:a, \(\dfrac{13}{2}\) = \(\dfrac{13\times5}{2\times5}\) = \(\dfrac{65}{10}\)
b, \(\dfrac{11}{40}\) = \(\dfrac{11\times25}{40\times25}\) = \(\dfrac{275}{1000}\)
c, \(\dfrac{21}{250}\) = \(\dfrac{21\times4}{250\times4}\) = \(\dfrac{84}{1000}\)
d, \(\dfrac{27}{45}\) = \(\dfrac{27:9}{45:9}\) = \(\dfrac{3}{5}\) = \(\dfrac{3\times2}{5\times2}\) = \(\dfrac{6}{10}\)
Bài 2:
a, (3\(\dfrac{1}{8}\) + 1\(\dfrac{3}{4}\)): 2\(\dfrac{1}{4}\)
= (\(\dfrac{25}{8}\) + \(\dfrac{7}{4}\)): \(\dfrac{9}{4}\)
= \(\dfrac{39}{8}\) \(\times\) \(\dfrac{4}{9}\)
= \(\dfrac{13}{6}\)
a) 10 x 18/27 x 15
= 2 x 5 x 2 x 9/3 x 9 x 3 x 5
= 4/9.
b) 1 x 2 x 3 x 4 x 5 x 6/7 x 8 x 9
= 1 x 2 x 3 x 4 x 5 x 3 x 2/7 x 2 x 4 x 3 x 3
= 1 x 5 x 2/ 7
= 10/7
c)\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}\)
\(=3\)
d) \(1\frac{1}{2}:1\frac{1}{3}:1\frac{1}{4}:1\frac{1}{5}=\frac{3}{2}:\frac{4}{3}:\frac{5}{4}:\frac{6}{5}=\frac{3}{2}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}=\frac{3}{4}\)
2. a) 0,123; 0,132; 0,213; 0,231; 0,312; 0,321.
b) 0,321; 0,312; 0,231; 0,213; 0,132; 0,123
3. 5 số đó là; 0,11;0,12;0,13;0,14;0,15
a) 0,11;0,12;0,13;0,14;0,15
b) 0,15;0,14;0,13;0,12;0,11
a) 2,(33)-5,01(4)+3,125
=2,333-5,014+3,125
=0,444
b) \(\left(8,21-3,\left(05\right)+1,2\right)\cdot3,\left(1\right)\)
\(=\left(8,21-3,050+1,2\right)\cdot3,111\)
\(=19,78596\)
c) \(\left(1,5+3,\left(5\right)\right):\left(2,1-3,2\right)\)
\(=\left(1,5+3,555\right):\left(-1,1\right)\)
\(=-\dfrac{5,055}{1,1}=-4,\left(5954\right)\)
a) \({4^6}.\sqrt {0,1} = 1295,2689\)
b) \(\sqrt[8]{{2,{1^{18}} + 1}} - \sqrt {2,{1^{12}} + 1} = - 80,4632\)
c) \(\frac{{1,{5^3}}}{{\sqrt[3]{{6,8}}}} = 1,7814\)