Tự dưng rén ngang :((

\(lim\dfrac{7^n+2^n}{3.7^n+4^n}=lim\dfrac{\dfrac{7^n}{7^n}+\dfrac{2^n}{7^n}}{\dfrac{3.7^n}{7^n}+\dfrac{4^n}{7^n}}=lim\dfrac{1+\left(\dfrac{2}{7}\right)^n}{3+\left(\dfrac{4}{7}\right)^n}=\dfrac{1}{3}\)

\(\left\{{}\begin{matrix}u_1+u_2+u_3=13\\u_4-u_1=26\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}u_1+u_1.q+u_1.q^2=13\\u_1.q^3-u_1=26\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}u_1\left(1+q+q^2\right)=13\\u_1\left(q^3-1\right)=26\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}u_1\left(1+q+q^2\right)=13\\u_1\left(q-1\right)\left(q^2+q+1\right)=26\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}13.\left(q-1\right)=26\\u_1.\left(q^3-1\right)=26\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}q=3\\u_1=1\end{matrix}\right.\)

\(S_8=\dfrac{u_1\left(1-q^8\right)}{1-q}=\dfrac{1.\left(1-3^8\right)}{1-3}=3280\)

\(a,lim\dfrac{5n+1}{2n}=lim\dfrac{\dfrac{5n}{n}+\dfrac{1}{n}}{\dfrac{2n}{n}}=lim\dfrac{5+\dfrac{1}{n}}{2}=\dfrac{5}{2}\\ b,lim\dfrac{6n^2+8n+1}{5n^2+3}=lim\dfrac{\dfrac{6n^2}{n^2}+\dfrac{8n}{n^2}+\dfrac{1}{n^2}}{\dfrac{5n^2}{n^2}+\dfrac{3}{n^2}}=lim\dfrac{6+\dfrac{8}{n}+\dfrac{1}{n^2}}{5+\dfrac{3}{n^2}}=\dfrac{6}{5}\)

\(c,lim\dfrac{3^n+2^n}{4.3^n}=\dfrac{\dfrac{3^n}{3^n}+\dfrac{2^n}{3^n}}{\dfrac{4.3^n}{3^n}}=\dfrac{1+\left(\dfrac{2}{3}\right)^n}{4}=\dfrac{1}{4}\)

\(d,lim\dfrac{\sqrt{n^2+5n+3}}{6n+2}=lim\dfrac{\sqrt{\dfrac{n^2+5n+3}{n^2}}}{\dfrac{6n}{n}+\dfrac{2}{n}}=lim\dfrac{\sqrt{1+\dfrac{5}{n}+\dfrac{3}{n^2}}}{6+\dfrac{2}{n}}=\dfrac{1}{6}\)

D

vòng này lỗi khá nhiều mình phải thoát bài mới tải đc ảnh :(( 

Diện tích là \(144^2\) hả bạn ??

\(a,5\left(2x-4\right)+20=10x-20+20=10x\\ b,\left(x-2\right)\left(2x+1\right)+x\left(1-2x\right)\\=2x^2-4x+x-2+x-2x^2\\ =\left(2x^2-2x^2\right)+\left(-4x+x+x\right)-2\\ =-2x-2\\ c,\left(x+1\right)^3+\left(x-1\right)\left(x^2+x+1\right)\\ =\left(x+1\right)^3+\left(x^3-1\right)\\ =x^3+3x^2+3x+1+x^3-1\\ =\left(x^3+x^3\right)+3x^2+3x+\left(1-1\right)\\ =2x^3+3x^2+3x\)

\(d,\left(x-y\right)^2+2x\left(x+y\right)\\ =x^2-2xy+y^2+2x^2+2xy\\ =\left(x^2+2x^2\right)+\left(-2xy+2xy\right)+y^2\\ =3x^2+y^2\)

sai hẳn 4 câu :0

\(3,\\ 65=5.13\\ 80=5.2^4\\ BCNN\left(65;80\right)=5.13.2^4=1040\\ 4,\\ 16=2^4\\ 25=5^2\\ 30=2.3.5\\ BCNN\left(16;25;30\right)=2^4.3.5^2=1200\)