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24 tháng 8 2023
`#040911`
`a,`
`15 + 25 \div (2x - 1) = 20`
`\Rightarrow 25 \div (2x - 1) = 20 - 15`
`\Rightarrow 25 \div (2x - 1) = 5`
`\Rightarrow 2x - 1 = 25 \div 5`
`\Rightarrow 2x - 1 = 5`
`\Rightarrow 2x = 6`
`\Rightarrow x = 3`
Vây, `x = 3.`
`b,`
\(3^{x-1}+2\cdot3^x=21\)
`\Rightarrow 3^x \div 3 + 2. 3^x = 21`
`\Rightarrow 3^x . \frac{1}{3} + 2. 3^x = 21`
`\Rightarrow 3^x . (\frac{1}{3} + 2) = 21`
`\Rightarrow 3^x . \frac{7}{3} = 21`
`\Rightarrow 3^x = 21 \div \frac{7}{3}`
`\Rightarrow 3^x = 9`
`\Rightarrow 3^x = 3^2`
`\Rightarrow x = 2`
Vậy, `x = 2.`
`c,`
\(2^{x-3}+2^{x+1}=17\)
`\Rightarrow 2^x \div 2^3 + 2^x . 2 = 17`
`\Rightarrow 2^x . \frac{1}{8} + 2^x . 2 = 17`
`\Rightarrow 2^x . (\frac{1}{8} + 2) = 17`
`\Rightarrow 2^x . \frac{17}{8} = 17`
`\Rightarrow 2^x = 17 \div \frac{17}{8}`
`\Rightarrow 2^x = 8`
`\Rightarrow 2^x = 2^3`
`\Rightarrow x = 3`
Vậy, `x = 3`
`d,`
\(5^x-5^{x-1}=20\)
`\Rightarrow 5^x - 5^x \div 5 = 20`
`\Rightarrow 5^x - 5^x . \frac{1}{5} = 20`
`\Rightarrow 5^x . (1 - \frac{1}{5} = 20`
`\Rightarrow 5^x . \frac{4}{5} = 20`
`\Rightarrow 5^x = 20 \div \frac{4}{5}`
`\Rightarrow 5^x = 25`
`\Rightarrow 5^x = 5^2`
`\Rightarrow x = 2`
Vậy, `x = 2.`
24 tháng 8 2023
\(a.25:\left(2x-1\right)=5\)
\(2x-1=5\Leftrightarrow2x=6\Leftrightarrow x=3\)
\(b.3^x:3+2.3^x=21\)\(\Leftrightarrow3^x.\dfrac{1}{3}+2.3^x=21\)
\(\Leftrightarrow3^x\left(\dfrac{1}{3}+2\right)=21\)
\(\Leftrightarrow3^x.\dfrac{7}{3}=21\)
\(\Leftrightarrow3^x=9\Leftrightarrow x=2\)
\(c.2^x:2^3+2^x.2=17\Leftrightarrow2^x.\dfrac{1}{8}+2^x.2=17\)
\(\Leftrightarrow2^x.\dfrac{17}{8}=17\Leftrightarrow2^x=8\Leftrightarrow x=3\)
\(d.5^x-5^x:5=20\Leftrightarrow5^x-5^x.\dfrac{1}{5}=20\)
\(\Leftrightarrow5^x\left(1-\dfrac{1}{5}\right)=20\Leftrightarrow5^x=20:\dfrac{4}{5}\Leftrightarrow5^x=25\Leftrightarrow x=2\)
18 tháng 7 2018
a) \(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-\frac{20}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{8}{11}=\frac{3}{11}\)
x = 1
b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\) ( nhân cho cả tử và mẫu của các số hạng trên ( ngoại trừ 2/x.(x+1) ) là 2)
\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)
\(2.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(2.\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\frac{1}{x+1}=\frac{1}{18}\)
=> x + 1 = 18
x = 17
18 tháng 7 2018
\(a,x-\left(\frac{20}{11.13}+\frac{20}{13.15}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(\Rightarrow x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Rightarrow x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Rightarrow x-\frac{8}{11}=\frac{3}{11}\)
\(\Rightarrow x=1\)
\(b,\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{18}=\frac{1}{x+1}\)
\(\Rightarrow x+1=18\Leftrightarrow x=17\)
4 tháng 4 2019
\(T=1\cdot2\cdot3+2\cdot3\cdot4+...+20\cdot21\cdot22\)
\(4T=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot4+...+20\cdot21\cdot22\cdot4\)
\(4T=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+..+20\cdot21\cdot22\cdot\left(23-19\right)\)
\(4T=0\cdot1\cdot2\cdot3-1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+..+20\cdot21\cdot22\cdot23-19\cdot20\cdot21\cdot22\)
\(4T=21\cdot22\cdot23\cdot24\)
\(T=\frac{21\cdot22\cdot23\cdot24}{4}=21\cdot22\cdot23\cdot6=63756\\ k.cho.mk.nha\)
4 tháng 4 2019
1.2.3+2.3.4+3.4.5+...+20.21.22
=1/4.(1.2.3.4+2.3.4.4+3.4.5.4+...+20.21.22.4)
=1/4.[1.2.3.(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+...+20.21.22.(23-19)]
=1/4.(1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+....-19.20.21.22+20.21.22.23)
=1/4.20.21.22.23
=53130
DT
0
NM
4 tháng 3 2021
-(1/3)-1/15-1/35-...-1/x.(x+2)=20/-21
=>1/3+1/15+1/35+...+1/x(x+2)=20/21
=>1/2 * (2/3 + 2/15 + 2/35 + ... + 2/x(x+2) )=20/21
=>\(\dfrac{2}{1\cdot3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{20}{21}:\dfrac{1}{2}\)
=>\(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{40}{41}\)
=>\(1-\dfrac{1}{x+2}=\dfrac{40}{41}\)
=>\(\dfrac{1}{x+2}=1-\dfrac{40}{41}=\dfrac{1}{41}\)
=>x+2=41=>x=39
TP
4 tháng 3 2021
(1/3)-1/15-1/35-...-1/x.(x+2)=20/-21
=>1/3+1/15+1/35+...+1/x(x+2)=20/21
=>1/2 * (2/3 + 2/15 + 2/35 + ... + 2/x(x+2) )=20/21
=>21⋅3+23.5+25.7+...+2x(x+2)=2021:1221⋅3+23.5+25.7+...+2x(x+2)=2021:12
=>1−13+13−15+15−17+...+1x−1x+2=40411−13+13−15+15−17+...+1x−1x+2=4041
=>1−1x+2=4041
HT
8 tháng 8 2015
\(x-\frac{20}{11.13}-\frac{20}{23.15}-....-\frac{20}{53.55}=\frac{3}{11}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+....+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-\frac{8}{11}=\frac{3}{11}\)
=> \(x=\frac{3}{11}+\frac{8}{11}=1\)
NP
1
NK
19 tháng 2 2016
Gọi số số hạng là n (n thuộc N*)
Ta có:
(21 + x)n : 2 = 0
=> (21 + x)n = 0
=> 21 + x = 0 (Vì n khác 0)
=> x = -21
x+(x+1)+(x+2)+...+(x+20)=21
=> 21x + ( 1+2+3+...+20) = 21
=> 21x + 210 = 21
=> 21x = -190
=> x= -190/21