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a)
Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:
2/9+6/27+8/36+12/54+16/72+18/81=
2/9+2/9+2/9+2/9+2/9+2/9=
2/9*6=
12/9=
4/3
Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3
b)
Ta có:
1-2/5=3/5
1-2/7=5/7
1-2/9=7/9
...
1-2/99=97/99
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=
3/5*5/7*7/9*...*97/99=
(3*5*7*...*97)/(5*7*9*...*99)=
3/99=
1/33
Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33
c)
Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:
S=1/2+1/4+1/8+1/16+...+1/1024
S*2=1+1/2+1/4+1/8+...+1/512
S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)
S=1-1/1024
S=1023/1024
Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024
4/3=1,333...
2015/2=1007,5
2/15=0,1333...
1023 /1024=0,9990234375
4056194 / 402999=10,06502249
1/8=0,125
sắp xếp từ bé đến lớn là:1/8;2/15;1023/1024;4/3;4056194 / 402999;2015/2
sắp xếp từ lớn đến bé là:2015/2;4056194 / 402999;4/3;1023/1024;2/15;1/8
\(1\dfrac{4}{5}+2\dfrac{5}{7}+3\dfrac{4}{5}+4\dfrac{5}{7}\)
\(\text{=}\left(1\dfrac{4}{5}+3\dfrac{4}{5}\right)+\left(2\dfrac{5}{7}+4\dfrac{5}{7}\right)\)
\(\text{=}1+3+\left(\dfrac{4}{5}+\dfrac{4}{5}\right)+2+4+\left(\dfrac{5}{7}+\dfrac{5}{7}\right)\)
\(\text{=}10+\dfrac{8}{5}+\dfrac{10}{7}\text{=}131\dfrac{1}{35}\)
a, 23/4 : 3 + 9/4 x 1/3 - 3/8
= 7,8 + 12,22 - 3,8
= 20,02 - 3,8
=16,22
b, 3/5 : 5/6 : 6/7 : 7/8 + 2/5 +23/35
=3/5 x 6/5 x 7/6 x 8/7 + 2/5 + 23/35
=24/25 + 2/5 + 23/35
=1/5 x(24/5 + 2 +23/7)
=1/5 x 353/35
=353/175
\(125,6+45,7:25\times5\) -> Nhân chia trước cộng trừ sau.
\(=125,6+1,828\times5\)
\(=125,6+9,14\)
\(=134,74\)
= \(\dfrac{31}{34}\)
Đặt \(A=\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+.......+\frac{1023}{1024}\)
\(\Rightarrow2A=1+\frac{3}{2}+\frac{7}{4}+......+\frac{1023}{512}\)
\(\Rightarrow2A-A=1+1+1+.......+1-\frac{1023}{1024}\)
\(\Rightarrow A=10-\frac{1023}{1024}=\frac{9217}{1024}\)