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\(S1=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{100.102}\)
\(S1=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{100.102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{51}{102}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\frac{25}{51}\)
\(S1=\frac{25}{102}\)
mk làm câu c cho nó dễ
c)1/1.2+1/2.3+...+1/x.(x+1)=2009/2010
=1-1/2+1/2-1/3+...+1/x-1/x+1=2009/2010
=1-1/x+1=2009/2010
=1/x+1=1-2009/2010
=1/x+1=1/2010
=) x+1=2010
x =2010-1
x =2009
tính :
a)\(\frac{459}{987}\cdot\left(\frac{1}{4}+\frac{1}{12}-\frac{1}{3}\right)-\frac{2009}{2010}\)
\(=\frac{459}{987}\cdot\left(\frac{3}{12}+\frac{1}{12}-\frac{4}{12}\right)-\frac{2009}{2010}\)
\(=\frac{459}{987}\cdot0-\frac{2009}{2010}\)
\(=\frac{-2009}{2010}\)
b) \(\frac{-9}{7}-\frac{5}{7}\cdot\left[\left(\frac{-2}{3}\right)^2-1\right]\div\frac{-5}{9}\)
\(=\frac{-9}{7}-\frac{5}{7}\cdot\left[\frac{4}{9}-1\right]\div\frac{-5}{9}\)
\(=\frac{-9}{7}-\frac{5}{7}\cdot\frac{-5}{9}\div\frac{-5}{9}\)
\(=\frac{-9}{7}-\frac{5}{7}\)
\(=-2\)
tìm x:
a) \(\left(x-\frac{7}{18}\right)-\frac{15}{27}=\frac{-10}{27}\)
\(\left(x-\frac{7}{18}\right)=\frac{-10}{27}+\frac{15}{27}\)
\(\left(x-\frac{7}{18}\right)=\frac{5}{27}\)
\(x=\frac{5}{27}+\frac{7}{18}\)
\(\Rightarrow x=\frac{31}{54}\)
b) \(\left(3\frac{1}{2}-2x\right)\cdot\frac{11}{3}=7\frac{1}{3}\)
\(\left(\frac{7}{2}-2x\right)\cdot\frac{11}{3}=\frac{22}{3}\)
\(\left(\frac{7}{2}-2x\right)=\frac{22}{3}\div\frac{11}{3}\)
\(\left(\frac{7}{2}-2x\right)=2\)
\(2x=\frac{7}{2}-2\)
\(x=\frac{3}{2}\div2=\frac{3}{4}\)
\(\Rightarrow x=\frac{3}{4}\)
1. a, M = -\(\dfrac{1}{3}.\dfrac{141}{17}-\dfrac{39}{3}.\left(-\dfrac{1}{17}\right)\)
= -\(\dfrac{1}{17}.\dfrac{141}{3}-\dfrac{39}{3}.\left(-\dfrac{1}{17}\right)\)
= -\(\dfrac{1}{17}\left(\dfrac{141}{3}-\dfrac{39}{3}\right)\)
= -\(\dfrac{1}{17}.34\)
= -2
@Lê Thị Hồng Ngát
1. b, \(\dfrac{3}{4}+\dfrac{1}{4}x=7\)
<=> \(\dfrac{1}{4}x=\dfrac{25}{4}\)
<=> x = 25
@Lê Thị Hồng Ngát
a) \(\left(x-1\right)^3=8=2^3\)
\(x-1=2\)
\(x=2+1=3\)
b) \(7^{2x-6}=49=7^2\)
\(2x-6=2\)
\(2x=6+2=8\)
\(x=8:2=4\)
c) \(\left(2x-14\right)^7=128=2^7\)
\(2x-14=2\)
\(2x=14+2=16\)
\(x=16:2=8\)
d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)
\(x=5\)
e) \(3\cdot\left(x+2\right):7\cdot4=120\)
\(x+2=120:3\cdot7:4\)
\(x+2=70\)
\(x=70-2=68\)
Lời giải:
a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$
$\Rightarrow x=3$
b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$
$\Rightarrow 2x=8$
$\Rightarrow x=4$
c. $(2x-14)^7=128=2^7$
$\Rightarrow 2x-14=2$
$\Rightarrow 2x=16$
$\Rightarrow x=18$
d.
$x^4.x^5=5^3.5^6$
$x^9=5^9$
$\Rightarrow x=5$
e.
$3(x+2):7=120:4=30$
$3(x+2)=30.7=210$
$x+2=210:3=70$
$x=70-2=68$
Bài 1:
a)12,5 x (-5/7) + 1,5 x (-5/7)
=-5/7*(12,5+1,5)
=-5/7*14
=-10
b)(-1/4) x (6|2/11) + 3|9/11 x (-1/4)
=-1/4*(68/11+42/11)
=-1/4*10
=-5/2
c tương tự
d)\(\frac{9^8\cdot4^3}{27^4\cdot6^5}=\frac{\left(3^2\right)^8\cdot\left(2^2\right)^3}{\left(3^3\right)^4\cdot\left(2\cdot3\right)^5}=\frac{3^{16}\cdot2^6}{3^{12}\cdot2^5\cdot3^5}=\frac{3^{16}\cdot2^5\cdot2}{3^{16}\cdot3^1\cdot2^5}=\frac{2}{3}\)
Bài 2:
a)Ta có:
2800=(28)100=256100
8200=(82)100=64100
Vì 256100>64100 =>2800>8200
b)Ta có:
1245=(123)15=172815
Vì 62515<172815 =>62515<1245