5n + 5n +2 = 650
3n +3 + 5.3 n = 864
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14 tháng 12 2023
5n+5n.52=650
5n(1+52)=650
5n.26=650
=>5n=650:26
=>5n=25=52
=>n=2
CD
1
NN
1
14 tháng 11 2017
a)
\(3^{n+1}+5.3^{n-2}=2592\)
\(\Rightarrow3^{n+1}+5.3^{n+1-3}=2592\)
\(\Rightarrow3^{n+1}+\dfrac{1}{27}.5.3^{n+1}=2592\)
\(\Rightarrow3^{n+1}+\dfrac{5}{27}.3^{n+1}=2592\)
\(\Rightarrow3^{n+1}.\left(\dfrac{5}{27}+1\right)=2592\)
\(\Rightarrow3^{n+1}.\dfrac{32}{27}=2592\)
\(\Rightarrow3^{n+1}=2187\)
\(\Rightarrow3^{n+1}=3^7\)
\(\Rightarrow n+1=7\)
\(\Rightarrow n=6\)
b)
\(3^{n+2}.5.3^{n-1}=864\)
\(\Rightarrow3^{n+2}+\dfrac{1}{27}.5.3^{n+2}=864\)
\(\Rightarrow3^{n+2}\left(\dfrac{5}{27}+1\right)=864\)
\(\Rightarrow3^{n+2}.\dfrac{32}{27}=864\)
\(\Rightarrow3^{n+2}=729\)
\(\Rightarrow3^{n+2}=3^6\)
\(\Rightarrow n+2=6\)
\(\Rightarrow n=4\)
JG
2
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
26 tháng 10 2023
\(3^{5n+2}+3^{5n+1}-3^{5n}=3^{5n}\left(3^2+3-1\right)=11.3^{5n}⋮11\)
4 tháng 11 2023
a: \(\lim\limits\dfrac{5n+1}{2n}=\lim\limits\dfrac{\dfrac{5n}{n}+\dfrac{1}{n}}{\dfrac{2n}{n}}=\lim\limits\dfrac{5+\dfrac{1}{n}}{2}=\dfrac{5+0}{2}=\dfrac{5}{2}\)
b: \(\lim\limits\dfrac{6n^2+8n+1}{5n^2+3}\)
\(=\lim\limits\dfrac{\dfrac{6n^2}{n^2}+\dfrac{8n}{n^2}+\dfrac{1}{n^2}}{\dfrac{5n^2}{n^2}+\dfrac{3}{n^2}}\)
\(=\lim\limits\dfrac{6+\dfrac{8}{n}+\dfrac{1}{n^2}}{5+\dfrac{3}{n^2}}\)
\(=\dfrac{6+0+0}{5+0}=\dfrac{6}{5}\)
c: \(\lim\limits\dfrac{3^n+2^n}{4\cdot3^n}\)
\(=\lim\limits\dfrac{\dfrac{3^n}{3^n}+\left(\dfrac{2}{3}\right)^n}{4\cdot\left(\dfrac{3^n}{3^n}\right)}\)
\(=\lim\limits\dfrac{1+\left(\dfrac{2}{3}\right)^n}{4}=\dfrac{1+0}{4}=\dfrac{1}{4}\)
d: \(\lim\limits\dfrac{\sqrt{n^2+5n+3}}{6n+2}\)
\(=\lim\limits\dfrac{\sqrt{\dfrac{n^2}{n^2}+\dfrac{5n}{n^2}+\dfrac{3}{n^2}}}{\dfrac{6n}{n}+\dfrac{2}{n}}\)
\(=\lim\limits\dfrac{\sqrt{1+\dfrac{5}{n}+\dfrac{3}{n^2}}}{6+\dfrac{2}{n}}\)
\(=\dfrac{\sqrt{1+0+0}}{6}=\dfrac{1}{6}\)
AD
4 tháng 11 2023
\(a,lim\dfrac{5n+1}{2n}=lim\dfrac{\dfrac{5n}{n}+\dfrac{1}{n}}{\dfrac{2n}{n}}=lim\dfrac{5+\dfrac{1}{n}}{2}=\dfrac{5}{2}\\ b,lim\dfrac{6n^2+8n+1}{5n^2+3}=lim\dfrac{\dfrac{6n^2}{n^2}+\dfrac{8n}{n^2}+\dfrac{1}{n^2}}{\dfrac{5n^2}{n^2}+\dfrac{3}{n^2}}=lim\dfrac{6+\dfrac{8}{n}+\dfrac{1}{n^2}}{5+\dfrac{3}{n^2}}=\dfrac{6}{5}\)
\(c,lim\dfrac{3^n+2^n}{4.3^n}=\dfrac{\dfrac{3^n}{3^n}+\dfrac{2^n}{3^n}}{\dfrac{4.3^n}{3^n}}=\dfrac{1+\left(\dfrac{2}{3}\right)^n}{4}=\dfrac{1}{4}\)
\(d,lim\dfrac{\sqrt{n^2+5n+3}}{6n+2}=lim\dfrac{\sqrt{\dfrac{n^2+5n+3}{n^2}}}{\dfrac{6n}{n}+\dfrac{2}{n}}=lim\dfrac{\sqrt{1+\dfrac{5}{n}+\dfrac{3}{n^2}}}{6+\dfrac{2}{n}}=\dfrac{1}{6}\)
a) 5n . 5n + 2 = 650
=> 5n + 5n . 52 = 650
=> 5n . (1 + 52) = 650
=> 5n . 26 = 650
=> 5n = 650 : 26
=> 5n = 25
=> 5n = 52
=> n = 2
b) 3n + 3 + 5.3n = 864
=> 3n . 33 + 5.3n = 864
=> 3n . (33 + 5) = 864
=> 3n . 32 = 864
=> 3n = 864 : 32
=> 3n = 27
=> 3n = 33
=> n = 3