2

\(S1=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{100.102}\)

\(S1=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{100.102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{51}{102}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\frac{25}{51}\)

\(S1=\frac{25}{102}\)

=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

2/

y=o

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

1.  x+1 =2x

x =1

xem họ nhà hứa có đúng k

Bài 2:

100! = 1.2.3.4.   ...................   .100

`#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`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)

`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.`