bài 1 : tính
\(B=\dfrac{1}{10.9}+\dfrac{1}{18.13}+\dfrac{1}{26.27}+...+\dfrac{1}{802.405}\)
\(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+...-\dfrac{1}{2^{58}}\)
mn giúp mk gấp nhé !!
Tính
a) A = \(\dfrac{1}{2.9}+\dfrac{1}{9.7}+\dfrac{1}{7.19}+...+\dfrac{1}{252.509}\)
b) B =\(\dfrac{1}{10.9}+\dfrac{1}{18.13}+\dfrac{1}{26.17}+...+\dfrac{1}{802.405}\)
c) C = \(\dfrac{2}{4.7}-\dfrac{3}{5.9}+\dfrac{2}{7.10}-\dfrac{3}{9.13}+...+\dfrac{2}{301.304}-\dfrac{3}{401.405}\)
giúp mk với
b)\(\dfrac{1}{7}B=\dfrac{1}{10.18}+\dfrac{1}{18.26}+\dfrac{1}{26.34}+...+\dfrac{1}{802.810}\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{8}{10.18}+\dfrac{8}{18.26}+\dfrac{8}{26.34}+...+\dfrac{8}{802.810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{34}+...+\dfrac{1}{802}-\dfrac{1}{810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}.\dfrac{8}{81}\)
\(\dfrac{1}{7}B=\dfrac{1.8}{8.81}\)
\(\dfrac{1}{7}B=\dfrac{1}{81}\)
\(B=\dfrac{1}{81}:\dfrac{1}{7}\)
\(B=\dfrac{7}{81}\)
Bài 9 : tính :
A = \(\dfrac{1}{2.9}\) +\(\dfrac{1}{9.7}\) +\(\dfrac{1}{7.19}\) +....+\(\dfrac{1}{252.509}\)
B = \(\dfrac{1}{10.9}\) + \(\dfrac{1}{18.13}\) + \(\dfrac{1}{26.17}\) + ... + \(\dfrac{1}{802.405}\)
a) \(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+...-\dfrac{1}{2^{58}}\)
\(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+....+\dfrac{1}{2^{55}}-\dfrac{1}{2^{58}}\\ \Rightarrow2^3D=\dfrac{1}{2^4}-\dfrac{1}{2^7}+\dfrac{1}{2^{10}}-\dfrac{1}{2^{13}}+...+\dfrac{1}{2^{58}}-\dfrac{1}{2^{61}}\\ \Rightarrow8D+D=\dfrac{1}{2}-\dfrac{1}{2^{61}}\\ \Rightarrow9D=\dfrac{1}{2}-\dfrac{1}{2^{61}}\\ \Rightarrow D=\dfrac{\dfrac{1}{2}-\dfrac{1}{2^{61}}}{9}\)
Bài 1. Tính
A= \(\left(8\dfrac{2}{7}-4\dfrac{2}{7}\right)-3\dfrac{4}{9}\)
B= \(\left(10\dfrac{2}{9}-6\dfrac{2}{9}\right)+2\dfrac{3}{5}\)
Bài 2. Tính
a) \(5\dfrac{1}{2}.3\dfrac{1}{4}\) b) \(6\dfrac{1}{3}:4\dfrac{2}{9}\) c) \(4\dfrac{3}{7}.2\)
`A=(8 2/7-4 2/7)-3 4/9`
`=8+2/7-4-2/7-3-4/9`
`=4-3-4/9`
`=1-4/9=5/9`
`B=(10 2/9-6 2/9)+2 3/5`
`=10+2/9-6-2/9+2+3/5`
`=4+2+3/5`
`=6+3/5=33/5`
Bài 2:
`a)5 1/2*3 1/4`
`=11/2*13/4`
`=143/8`
`b)6 1/3:4 2/9`
`=19/3:38/9`
`=19/3*9/38=3/2`
`c)4 3/7*2`
`=31/7*2`
`=62/7`
Bài 1:
\(A=\left(8\dfrac{2}{7}-4\dfrac{2}{7}\right)-3\dfrac{4}{9}\)
\(A=\left(\dfrac{58}{7}-\dfrac{30}{7}\right)-\dfrac{31}{9}\)
\(A=4-\dfrac{31}{9}\)
\(A=\dfrac{5}{9}\)
\(B=\left(10\dfrac{2}{9}-6\dfrac{2}{9}\right)+2\dfrac{3}{5}\)
\(B=\left(\dfrac{92}{9}-\dfrac{56}{9}\right)+\dfrac{13}{5}\)
\(B=4+\dfrac{13}{5}\)
\(B=\dfrac{33}{5}\)
Bài 2:
a) \(5\dfrac{1}{2}.3\dfrac{1}{4}=\dfrac{11}{2}.\dfrac{13}{4}=\dfrac{11.13}{2.4}=\dfrac{143}{8}\)
b) \(6\dfrac{1}{3}:4\dfrac{2}{9}=\dfrac{19}{3}:\dfrac{38}{9}=\dfrac{19}{3}.\dfrac{9}{38}=\dfrac{3}{2}\)
c) \(4\dfrac{3}{7}.2=\dfrac{31}{7}.2=\dfrac{31.2}{7}=\dfrac{62}{7}\)
Bài 1: Thực hiện phép tính
a) \(1-\dfrac{1}{2}+\dfrac{1}{3}\)
b) \(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}\)
c) \(\dfrac{7}{11}.\dfrac{3}{4}+\dfrac{7}{11}.\dfrac{1}{4}+\dfrac{4}{11}\)
d) \(\left(\dfrac{3}{4}+0,5+25\%\right).2\dfrac{2}{3}\)
\(Bài 2:\text{Tìm x}\)
a) \(x+\dfrac{1}{2}=2\)
b) \(75\%x-\dfrac{1}{2}=-1\dfrac{1}{4}\)
c) \(\left|x-\dfrac{2}{5}\right|+\dfrac{7}{10}=3\)
a) \(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{6-3+2}{6}=\dfrac{1}{6}\)
\(b.\) \(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{6+10}{15}=\dfrac{16}{15}\)
\(c.\) \(\dfrac{7}{11}.\dfrac{3}{4}+\dfrac{7}{11}.\dfrac{1}{4}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{16}{44}=\dfrac{21+7+16}{44}=\dfrac{44}{44}=1\)
a/\(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)
b/\(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{16}{15}\)
d) \(\left(\dfrac{3}{4}+0,5+25\%\right).2\dfrac{2}{3}=\left(\dfrac{3}{4}+\dfrac{1}{2}+\dfrac{1}{4}\right).\dfrac{8}{3}=\left(\dfrac{3}{4}+\dfrac{2}{4}+\dfrac{1}{4}\right).\dfrac{8}{3}=\dfrac{3}{2}.\dfrac{8}{3}=4\)
chỉ mk với các bạn mk đang cần gấp lắm
\(\dfrac{1}{2022}x\dfrac{2}{5}+\dfrac{1}{2022}x\dfrac{7}{5}-\dfrac{1}{2022}x\dfrac{8}{10}\)
cố gắng giải giúp mk nhé các bạn !!!!
\(\dfrac{1}{2022}\) \(\times\) \(\dfrac{2}{5}\) + \(\dfrac{1}{2022}\) \(\times\) \(\dfrac{7}{5}\) - \(\dfrac{1}{2022}\) \(\times\) \(\dfrac{8}{10}\)
= \(\dfrac{1}{2022}\) \(\times\) ( \(\dfrac{2}{5}\) + \(\dfrac{7}{5}\) - \(\dfrac{8}{10}\))
= \(\dfrac{1}{2022}\) \(\times\) ( \(\dfrac{9}{5}\) - \(\dfrac{4}{5}\))
= \(\dfrac{1}{2022}\) \(\times\) \(\dfrac{5}{5}\)
= \(\dfrac{1}{2022}\times1\)
= \(\dfrac{1}{2022}\)
rút gọn
a.\(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}\)
b.\(\dfrac{6}{\sqrt{5}-1}+\dfrac{7}{1-\sqrt{3}}-\dfrac{2}{\sqrt{3}-\sqrt{5}}\)
lm mhanh giúp mk nhé!mk đang cần gấp!
`a)(5sqrt2-2sqrt5)/(sqrt5-sqrt2)+6/(2-sqrt{10})`
`=(sqrt{10}(sqrt5-sqrt2))/(sqrt5-sqrt2)+(6(2+sqrt{10}))/(4-10)`
`=sqrt{10}-(2+sqrt{10})`
`=-2`
`b)6/(sqrt5-1)+7/(1-sqrt3)-2/(sqrt3-sqrt5)`
`=(6(sqrt5+1))/(5-1)+(7(1+sqrt3))/(1-3)-(2(sqrt3+sqrt5))/(3-5)`
`=(6(sqrt5+1))/4-(7+7sqrt3)/2+sqrt3+sqrt5`
`=(3sqrt5+3)/2-(7+7sqrt3)/2+sqrt3+sqrt5`
`=(3sqrt5+3-7-7sqrt3+2sqrt3+2sqrt5)/2`
`=(5sqrt5-5sqrt3-4)/2`
\(\text{Bài 4. Chứng tỏ rằng:}\)
\(a\)) \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{30^2}< 1\)
\(b\)) \(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{99}+\dfrac{1}{100}>1\)
\(c\)) \(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}< 2\)
\(d\)) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{29.30}< 1\)
a)
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{30^2}\\ < \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{29.30}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{29}-\dfrac{1}{30}\\ =1-\dfrac{1}{30}=\dfrac{29}{30}< 1\left(dpcm\right)\)
b)
\(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{99}+\dfrac{1}{100}=\dfrac{1}{10}+\left(\dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{99}+\dfrac{1}{100}\right)\\ >\dfrac{1}{10}+\dfrac{1}{100}+\dfrac{1}{100}+...+\dfrac{1}{100}=\dfrac{1}{10}+\dfrac{90}{100}\\ =\dfrac{110}{100}>1\left(đpcm\right).\)
c)
\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{17}\\ =\left(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}\right)+\left(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{17}\right)\\ < \dfrac{1}{5}.5+\dfrac{1}{8}.8=1+1=2\left(đpcm\right)\)
d) tương tự câu 1
Bài 1 : Thực hiện phép tính ( tính hợp lý nếu có thể )
a ) \(\dfrac{1}{12}+\dfrac{3}{4}\)
b ) \(\dfrac{-4}{7}.1\dfrac{1}{2}\)
c )\(\dfrac{7}{9}+\left(\dfrac{2}{3}+\dfrac{-7}{9}\right)\)
d )\(\dfrac{2}{3}-\dfrac{1}{3}:\dfrac{3}{4}\)
e )\(\dfrac{-7}{25}.\dfrac{11}{13}+\dfrac{-7}{25}.\dfrac{2}{13}\)
g )\(2\dfrac{2}{5}.0,25-\left(\dfrac{11}{20}+75\%\right):\dfrac{13}{5}\)
a. 1/12 + 3/4
= 1/12+ 9/12
= 10/12 = 5/6
b. -4/7. 1 1/2
= -4/7. 3/2
= -6/7
c. 7/9+ ( 2/3 + -7/9)
= 7/9 + -1/9
= 8/9 = 2/3
d. 2/3 - 1/3 : 3/4
= 2/3 - 4/9
= 6/9 - 4/9
= 2/9
e. -7/25 . 11/13+ - 7/25. 2/13
=-77/ 325+ -14/ 325
= - 7/25
g. 2 2/5 . 0,25- ( 11/20+ 75%) : 13/5
= 12/5 . 1/4 - ( 11/20 + 3/4) : 13/5
= 12/5 . 1/4 - 13/10 : 12/ 5
= 3/5 - 13/24
= 7/120
lm đại vậy thôi nha hơi lâu vì mik bị lag nên phải làm lại