1 + [ 2/3 + 3/4 + 4/5 - 1/1/3 - 2 * x ] * 4 = 4
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a) Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A=\left(\frac{1}{2}\times2\right)+\left(\frac{1}{4}\times2\right)+\left(\frac{1}{8}\times2\right)+\left(\frac{1}{16}\times2\right)+\left(\frac{1}{32}\times2\right)\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
Ta lấy : \(2A-1A=1A\)
\(A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(A=1-\frac{1}{32}\)
\(A=\frac{31}{32}\)
Vậy \(A=\frac{31}{32}\)
b) Đặt \(B=\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{18\times19}+\frac{2}{19\times20}\)
\(B=2\times(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20})\)
\(B=2\times\left(1-\frac{1}{20}\right)\)
\(B=2\times\frac{19}{20}\)
\(B=\frac{19}{10}\)
Vậy \(B=\frac{19}{10}\)
Học tốt # ^-<
ta có:
\(abc5-1107=5abc\)
\(1107=abc5-5abc\)
\(\Rightarrow abc5-5abc=1107\)
\(\Rightarrow abc\cdot10+5-5000-abc=1107\)
\(abc\cdot10-abc=1107+5000-5\)
\(abc\cdot9=6102\)
\(abc=6102:9=678\)
VẬY \(abc=678\)
TK MK NHA. ^_^
abc2- 2abc = 2142
abc x 10 + 2 - abc + 2000 = 2142
abc x 10 + 2 - abc = 2142 + 2000
abc x 10 + 2 - abc = 4142
abc x 9 = 4142 - 2
abc x 9 = 4140
abc = 4140 : 9
abc = 460
Vậy abc = 460
2-c=2 => c=0
ab02-2ab0=2142
0-b=4 (nhớ 1) => b=6
a602-2a60=2142
5-a=1 => a=4
nên abc=460
1abcd x 5 =abcd5
(10000+abcd).5=abcd.10+5
50000+5.abcd=10.abcd+5
5.abcd=50000-5
abcd=49995:5
abcd=9999
Mik ko bt đúng ko nhưng hok tốt !
Gọi số cần tìm là \(\overline{abcd}\)(a khác 0: a,b,c,d <10)
Ta có: \(\overline{abcd5}\)=5x \(\overline{1abcd}\)
\(\overline{abcd}\)x 10 +5 = 5 x (10000 + \(\overline{abcd}\))
\(\overline{abcd}\) x 10 + 5 = 50000 + 5 x \(\overline{abcd}\)
\(\overline{abcd}\)x 10 -5 x \(\overline{abcd}\)= 50000 - 5
\(\overline{abcd}\) x 5 = 49995
\(\overline{abcd}\)= 49995 : 5 = 9999
Vậy số cần tìm là 9999.
\(58\cdot42+32\cdot58\cdot26\)
\(=58\cdot42+58\cdot832\)
\(=58\cdot\left(42+832\right)\)
\(=58\cdot874\)
\(=50692\)