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17 tháng 4 2019
2
\(S1=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{100.102}\)
\(S1=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{100.102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\left(\frac{51}{102}-\frac{1}{102}\right)\)
\(S1=\frac{1}{2}.\frac{25}{51}\)
\(S1=\frac{25}{102}\)
28 tháng 6 2018
=a, \(\dfrac{x}{15}\) = \(\dfrac{2}{5}\)
= \(x.5=15.2\)
=> \(x=\dfrac{15.2}{5}\)\(=\dfrac{30}{5}\) \(=6\)
Vậy \(x=6\)
b, \(\dfrac{3}{x-7}\) \(=\dfrac{27}{135}\)
= \(\dfrac{3}{x-7}\) \(=\dfrac{3}{15}\)
= \(x-7=15\)
\(x=15+7\)
\(x=22\)
vậy x = 22
c, \(320.x-10=5.48:24\)
= \(320x-10=240:24\)
= \(320x-10=10\)
= \(320x=10+10\)
\(320x=20\)
\(x=20:320\)
\(x=0,0625\)
d, \(5x-1952=\) \(2500-1947\)
\(5x-1952=553\)
\(5x=553+1952\)
\(5x=2505\)
\(x=2505:5\)
\(x=501\)
e, \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+\left(x+4\right)\left(x+5\right)=45\)
= \(\left(x+x+x+x+x\right)\)+\(\left(1+2+3+4+5\right)\) \(=45\)
= \(5x+15=45\)
\(5x=45-15\)
\(5x=30\)
\(x=30:5\)
\(x=6\)
f, \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}-\dfrac{2}{63}=\dfrac{1}{9}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}=\dfrac{1}{9}+\dfrac{2}{63}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}-\dfrac{2}{35}=\dfrac{1}{7}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}=\dfrac{1}{7}+\dfrac{2}{35}\)
= \(x-\dfrac{2}{3}-\dfrac{2}{15}=\dfrac{1}{5}\)
= \(x-\dfrac{2}{3}=\dfrac{1}{5}+\dfrac{2}{15}\)
= \(x-\dfrac{2}{3}=\dfrac{1}{3}\)
\(x=\) \(\dfrac{1}{3}+\dfrac{2}{3}\)
\(x=1\)
k, \(\dfrac{3+5+7+...+2015}{2+4+6+...+2014+x}=1\)
ta thấy phần tử là tập hợp các số lẻ ; phần mẫu là tập hợp các số chẵn
mà số chẵn hơn số lẻ 1 đơn vị
nên x thuộc tổng các số phần tử hơn mẫu là 1 đơn vị
=> từ \(2+4+6+...+2014\)có số số hạng là :
( 2014 - 2 ) : 2 + 1 = 1007
vậy x sẽ bằng :
( 1 + 1 ) . 1007 : 2 = 1007
vập số cần tìm là : 1007
6 tháng 8 2022
a: \(\Leftrightarrow\left(\dfrac{13}{4}:x\right)\cdot\left(-\dfrac{5}{4}\right)=\dfrac{-10}{6}-\dfrac{5}{6}=\dfrac{-15}{6}=\dfrac{-5}{2}\)
\(\Leftrightarrow\dfrac{13}{4}:x=\dfrac{5}{2}\cdot\dfrac{5}{4}=\dfrac{25}{8}\)
hay \(x=\dfrac{13}{4}:\dfrac{25}{8}=\dfrac{13}{4}\cdot\dfrac{8}{25}=\dfrac{26}{25}\)
b: \(\Leftrightarrow\dfrac{3}{4}:x=\dfrac{11}{36}-\dfrac{1}{4}=\dfrac{2}{36}=\dfrac{1}{18}\)
=>\(x=\dfrac{3}{4}:\dfrac{1}{18}=\dfrac{54}{4}=\dfrac{27}{2}\)
c: \(\Leftrightarrow\left(-\dfrac{6}{5}+x\right):\left(-3.6\right)=-\dfrac{7}{4}+\dfrac{1}{4}\cdot8=\dfrac{1}{4}\)
=>x-6/5=-9/10
=>x=3/10
24 tháng 9 2023
`#3107`
b)
`2.3^x = 162`
`\Rightarrow 3^x = 162 \div 2`
`\Rightarrow 3^x = 81`
`\Rightarrow 3^x = 3^4`
`\Rightarrow x = 4`
Vậy, `x = 4`
c)
`(2x - 15)^5 = (2 - 15)^3`
\(\Rightarrow \)`(2x - 15)^5 - (2x - 15)^3 = 0`
\(\Rightarrow \)`(2x - 15)^3 . [ (2x - 15)^2 - 1] = 0`
\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=15\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x-15=1\\2x-15=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x=16\\2x=-14\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=-7\end{matrix}\right.\)
Vậy, `x \in`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)
24 tháng 9 2023
`d)`
\(3^{x+2}-5.3^x=?\) Bạn ghi tiếp đề nhé!
`e)`
\(7\cdot4^{x-1}+4^{x-1}=23?\)
\(4^{x-1}\cdot\left(7+1\right)=23\\ \Rightarrow4^{x-1}\cdot8=23\\ \Rightarrow4^{x-1}=\dfrac{23}{8}\)
Bạn xem lại đề!
`f)`
\(2\cdot2^{2x}+4^3\cdot4^x=1056\)
\(\Rightarrow2\cdot2^{2x}+\left(2^2\right)^3\cdot\left(2^2\right)^x=1056\\ \Rightarrow2\cdot2^{2x}+2^6\cdot2^{2x}=1056\\ \Rightarrow2^{2x}\cdot\left(2+2^6\right)=1056\\ \Rightarrow2^{2x}\cdot66=1056\\ \Rightarrow2^{2x}=1056\div66\\ \Rightarrow2^{2x}=16\\ \Rightarrow2^{2x}=2^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)
Vậy, `x = 2`
_____
\(10 -{[(x \div 3+17) \div 10+3.2^4] \div 10}=5\)
\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)
\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)
\(\Rightarrow\left(x\div3+17\right)\div10+48=50\)
\(\Rightarrow\left(x\div3+17\right)\div10=2\)
\(\Rightarrow x\div3+17=20\)
\(\Rightarrow x\div3=3\\ \Rightarrow x=9\)
Vậy, `x = 9.`
NH
3
H
19 tháng 5 2021
1. \(\dfrac{2019}{2020}-\left(\dfrac{2019}{2020}-\dfrac{2020}{2021}\right)\)
\(=\dfrac{2019}{2020}-\dfrac{2019}{2020}+\dfrac{2020}{2021}\)
\(=0+\dfrac{2020}{2021}=\dfrac{2020}{2021}\)
19 tháng 5 2021
Giải:
1) \(\dfrac{2019}{2020}-\left(\dfrac{2019}{2020}-\dfrac{2020}{2021}\right)\)
\(=\dfrac{2019}{2020}-\dfrac{2019}{2020}+\dfrac{2020}{2021}\)
\(=\left(\dfrac{2019}{2020}-\dfrac{2019}{2020}\right)+\dfrac{2020}{2021}\)
\(=0+\dfrac{2020}{2021}\)
\(=\dfrac{2020}{2021}\)
2) \(\dfrac{2}{9}+\dfrac{7}{9}:\left(\dfrac{42}{5}-\dfrac{7}{5}\right)\)
\(=\dfrac{2}{9}+\dfrac{7}{9}:7\)
\(=\dfrac{2}{9}+\dfrac{1}{9}\)
\(=\dfrac{1}{3}\)
3) \(\dfrac{3}{4}+\dfrac{x}{4}=\dfrac{5}{8}\)
\(\dfrac{x}{4}=\dfrac{5}{8}-\dfrac{3}{4}\)
\(\dfrac{x}{4}=\dfrac{-1}{8}\)
\(\Rightarrow x=\dfrac{4.-1}{8}=\dfrac{-1}{2}\)
4) \(\left|3x+1\right|-\dfrac{1}{4}=\dfrac{-1}{4}\)
\(\left|3x-1\right|=\dfrac{-1}{4}+\dfrac{1}{4}\)
\(\left|3x-1\right|=0\)
\(3x-1=0\)
\(3x=0+1\)
\(3x=1\)
\(x=1:3\)
\(x=\dfrac{1}{3}\)
Chúc bạn học tốt!