\(1+3+..+3^n=\dfrac{3^{n+1}-1}{3-1}=\dfrac{3^{n+1}-1}{2}\)
\(1+2+...+2^n=\dfrac{2^{n+1}-1}{2-1}=2^{n+1}-1\)
\(I=\lim\limits\dfrac{3^{n+1}-1}{2.2^{n+1}-2}=\lim\dfrac{\left(\dfrac{3}{2}\right)^{n+1}-\left(\dfrac{1}{2}\right)^{n+1}}{2-2\left(\dfrac{1}{2}\right)^{n+1}}=\dfrac{+\infty}{2}=+\infty\)
Cho các số x,y,z thỏa mãn:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4};2x+3y-z=95\)
Khi đó, x+y+z bằng bao nhiêu?
\(lim\dfrac{2^{n+1}+3n+10}{3n^2-n+2}\)
tính \(\lim\limits_{x\rightarrow+\infty}\) \(\dfrac{\left(x+1\right)\left(x^2+1\right)\left(x^3+1\right)...\left(x^{11}+1\right)}{[\left(11x\right)^{11}+1]^6}\)
\(f\left(n\right)=\left(n^2+n+1\right)^2+1\). Xét dãy \(\left(u_n\right)\) sao cho : \(\left(u_n\right)=\dfrac{f\left(1\right)\cdot f\left(3\right)\cdot f\left(5\right)...\cdot f\left(2n-1\right)}{f\left(2\right)\cdot f\left(4\right)\cdot...\cdot f\left(2n\right)}\). Tính \(\lim\limits_{n\sqrt{u_n}}\)
giá trị của B = lim (2n+3)/(n^2 + 1) =
