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1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
=1/(2.3)+1/(3.4)+1/(4.5) + 1/(5.6)+ 1/(6.7)+1/(7.8)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/5-1/6+1/6-1/7+1/7-1/8
=1-1/8
=7/8
= 1/(2.3) + 1/(3.4) + 1/(4.5) + 1/(5.6) + 1/(6.7) + 1/(7.8)
= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8
= 1/2 - 1/8
= 3/8
làm được câu a thui
\(\frac{1}{100}=\frac{1}{10.10}\);\(\frac{1}{90}=\frac{1}{9.10}\);...
Suy ra \(\frac{1}{10.10}-\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-...-\frac{1}{1.2}\)
\(\frac{1}{10}-\frac{1}{10}-\frac{1}{10}-\frac{1}{9}-...-1-\frac{1}{2}\)
\(\frac{1}{10}-\frac{1}{2}\)
\(-\frac{4}{10}\)
Bài 1:
a) A=1+22+24+.................+2100
2A=(1+22+24+.................+2100)
2A=2+23+...+2101
2A-A=(2+23+...+2101)-(1+22+24+.................+2100)
A=2101-1
b)bạn tự làm
c) C=-1/90-1/72-1/50-1/42-1/30-1/20-1/12-1/6-1/2
\(=-\left(\frac{1}{90}+\frac{1}{72}+...+\frac{1}{2}\right)\)
\(=-\left(\frac{1}{10.9}+\frac{1}{9.8}+...+\frac{1}{2.1}\right)\)
\(=-\left(\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{8}+...+\frac{1}{2}-1\right)\)
\(=-\left(\frac{1}{10}-1\right)\)
\(=-\left(-\frac{9}{10}\right)=\frac{9}{10}\)
Bài 2:
cứ tính lần lượt là ra
a) \(A=\dfrac{3}{5}+6\dfrac{5}{6}+\left(11\dfrac{5}{20}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)
\(=\dfrac{3}{5}+\dfrac{41}{6}\left(11\dfrac{1}{4}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)
\(=\dfrac{3}{5}+\dfrac{41}{6}.2.\dfrac{3}{25}\)
\(=\dfrac{3}{5}+\dfrac{41}{25}\)
\(=\dfrac{15}{25}+\dfrac{41}{25}\)
\(=\dfrac{56}{25}\)
a) A = \(\dfrac{3}{5}+6\dfrac{5}{6}\left(11\dfrac{5}{20}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)
A = \(\dfrac{3}{5}+\dfrac{41}{6}\) \(\left(\dfrac{45}{4}-\dfrac{37}{4}\right)\) : \(\dfrac{25}{3}\)
A = \(\dfrac{3}{5}+\dfrac{41}{6}\) . 2 : \(\dfrac{25}{3}\)
A = \(\dfrac{3}{5}\) + \(\dfrac{41}{3}\) : \(\dfrac{25}{3}\)
A = \(\dfrac{3}{5}\) + \(\dfrac{41}{25}\)
A = \(\dfrac{56}{25}\)
A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8
A = 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8
A = 1 + ( -1/2 + 1/2 ) + ( -1/3 + 1/3 ) + ( -1/4 + 1/4 ) + ( -1/5 + 1/5 ) + ( -1/6 + 1/6 ) + ( -1/7 + 1/7 ) - 1/8
A = 1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8
A = 1 - 1/8
A = 7/8
* Sửa đề tí nhé
B = 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56
B = 3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8
B = 3 - 3/2 - 5/2 - ( -5/3 ) + 7/3 - 7/4 - 9/4 - ( -9/5 ) + 11/5 - 11/6 - 13/6 - ( -13/7 ) + 15/7 - 15/8
B = 3 - 3/2 - 5/2 + 5/3 + 7/3 - 7/4 - 9/4 + 9/5 + 11/5 - 11/6 - 13/6 + 13/7 + 15/7 - 15/8
B = 3 + ( -3/2 - 5/2 ) + ( 5/3 + 7/3 ) + ( -7/4 - 9/4 ) + ( 9/5 + 11/5 ) + ( -11/6 - 13/6 ) + ( 13/7 + 15/7 ) - 15/8
B = 3 + -4 + 4 + -4 + 4 + -4 + 4 - 15/8
B = 3 + 0 + 0 + 0 - 15/8
B = 3 - 15/8
B = 9/8
a) 7/10+6/10\(=\frac{13}{10}\)
b) -5/9+2/9\(=\frac{-1}{3}\)
c)1/7+1 6/7\(=2\)
d) 3/13+10/3+1\(=\frac{71}{26}\)
e) 5/12-7/12\(=\frac{-1}{6}\)
f) 7/6+5/6-1/6\(=\frac{11}{6}\)
g) -3/20+7/20-9/20\(=\frac{-1}{4}\)
học tốt
b) 89−172−156−142−130−120−112−16−1289−172−156−142−130−120−112−16−12
=89−(172+156+142+130+120+112+16+12)89−(172+156+142+130+120+112+16+12)
=89−(18−19+17−18+...+12−13+12)=89−89=0