\(S=1\cdot4+2\cdot5+3\cdot6+...+100\cdot103\)

\(=1\cdot\left(2+2\right)+2\cdot\left(3+2\right)+...+100\cdot\left(101+2\right)\)

\(=1\cdot2+1\cdot2+2\cdot3+2\cdot2+...+100\cdot101+100\cdot2\)

\(=\left(1\cdot2+2\cdot3+3\cdot4+..+100\cdot101\right)+\left(2+4+6+...+200\right)\)

\(=\frac{100\cdot101\cdot102}{3}+\frac{200\cdot\left(200+2\right):2}{2}=343400+10100=353500\)

\(\frac{3}{2x-4}=\frac{1}{x+2}\)

\(\Rightarrow\left(x+2\right)\cdot3=\left(2x-4\right)\cdot1\)

\(\Rightarrow3x+6=2x-4\)

\(\Rightarrow3x-2x=-4-6\)

\(\Rightarrow1x=-10\)

\(\Rightarrow x=-10\)

\(\frac{3}{2x-4}=\frac{1}{x+2}\)

\(\Rightarrow3\left(x+2\right)=2x-4\)

\(\Rightarrow3x+6=2x-4\)

\(\Rightarrow3x-2x=-4-6\)

\(\Rightarrow x=-10\)

học tốt ~~~

a. \(\frac{2-2a}{6-8b}=\frac{3-3a}{9-12b}\)

\(\Leftrightarrow\left(6-8b\right)\left(3-3a\right)=\left(2-2a\right)\left(9-12b\right)\)

\(\Leftrightarrow18-18a-24b+24ab=18-24b-18a+24ab\) ( đúng )

=> Đpcm

b. Gọi d là ƯCLN của n + 3 và 2n + 5

n + 3 chia hết cho d

2n + 5 chia hết cho d

\(\Rightarrow\left(n+3\right)-\left(2n+5\right)⋮d\)

\(\Rightarrow2\left(n+3\right)-2n-5⋮d\)

\(\Rightarrow2n+6-2n-5⋮d\)

\(\Rightarrow1⋮d\)=> d = 1

=> Đpcm

a) Giả sử \(\frac{2-2a}{6-8b}=\frac{3-3a}{9-12b}\)là đúng

Ta cần chứng minh \(\frac{2-2a}{6-8b}-\frac{3-3a}{9-12b}=0\)

\(\Rightarrow\frac{2\left(1-a\right)}{2\left(3-4b\right)}-\frac{3\left(1-a\right)}{3\left(3-4b\right)}=0\)

\(\Rightarrow\frac{1-a}{3-4b}-\frac{1-a}{3-4b}=0\)( đúng )

Vậy ta có đpcm

b) Gọi d là ƯCLN( n + 3 ; 2n + 5 )

\(\Rightarrow\hept{\begin{cases}n+3⋮d\\2n+5⋮d\end{cases}}\Rightarrow\hept{\begin{cases}2\left(n+3\right)⋮d\\2n+5⋮d\end{cases}}\Rightarrow\hept{\begin{cases}2n+6⋮d\\2n+5⋮d\end{cases}}\)

\(\Rightarrow\left(2n+6\right)-\left(2n+5\right)⋮d\)

\(\Rightarrow2n+6-2n-5⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d=1\)

\(\RightarrowƯCLN\left(n+3;2n+5\right)=1\)

\(\Rightarrow\frac{n+3}{2n+5}\)là phân số tối giản ( đpcm )

\(\left|2x-7\right|=20+5\cdot\left(-3\right)\)

\(\left|2x-7\right|=20+\left(-15\right)\)

\(\left|2x-7\right|=5\)

\(\Rightarrow\orbr{\begin{cases}2x-7=-5\\2x-7=5\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=6\end{cases}}\)

=> |2x-7| = 5

=> 2x-7=-5 hoặc 2x-7=5

=> x=1 hoặc x=6

Vậy .........

Tk mk nha

\(\frac{1}{7}-\frac{8}{7}:8-3:\frac{3}{4}x\left(-2\right)^2\)

\(=\frac{1}{7}-\frac{1}{7}-4x4\)

\(=0-16=-16\)

học tốt ~~~

= 1/7-1/7-4*2

=0-4*2

=0-8=-8

tao dóe biet

a,1^2/1.2 . 2^2/2.3 . 3^2/3.4 ... 99^2/99.100 . 100^2/100.101

= 1/2 . 2/3 . 3/4 ... 99/100 . 100/101

=( 2.3.4....100/2.3.4...100) . 1/101

= 1 . 1/101

=1/101

ý b tương tự nhé !