a,\(\frac{16}{2^n}\)=2
b, \(\frac{\left(-3^n\right)}{81}\)= -27
c, 8n : 2n =4
Những câu hỏi liên quan
lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
lim \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\)
lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
a) lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
= lim \(\frac{\left(2-\frac{3}{n}+\frac{5}{n^2}\right)\left(2+\frac{1}{n}\right)}{\left(\frac{4}{n}-3\right)\left(2+\frac{1}{n}+\frac{1}{n^2}\right)}=\frac{4}{-6}=-\frac{2}{3}\)
b)lim ( \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\))
= lim ( \(\frac{n\sqrt{n^4+1}-\sqrt{4n^6+2}}{n^2}\) )
= lim \(\frac{\left(n^6+n^2\right)-\left(4n^6+2\right)}{n^2\left(n\sqrt{n^4+1}+\sqrt{4n^2+2}\right)}\)
= lim \(\frac{-3n^6+n^2+2}{n^3\sqrt{n^4+1}+n^2\sqrt{4n^2+2}}\)
= lim \(\frac{-3n\left(1-\frac{1}{n^4}-\frac{2}{n^6}\right)}{\sqrt{1+\frac{1}{n^4}}+\frac{1}{n^2}\sqrt{4+\frac{2}{n^2}}}\)
= lim \(-3n=-\infty\)
c) lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
= lim\(\frac{2+\frac{3}{n}}{\sqrt{9+\frac{3}{n^2}}-\sqrt[3]{\frac{2}{n}-8}}=\frac{2}{3+2}=\frac{2}{5}\)
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5/ lim \(\frac{\left(12-n\right)^3\left(n-2\right)}{\sqrt{n^8-1}-2n^4}\)
6/ lim \(\frac{\sqrt[3]{3-8n^3}-n}{2n+5}\)
7/ lim \(\frac{\sqrt{n^6-2n+1}}{\sqrt{4n^6+3n}}\)
8/ lim \(\left(n^4+2n-20\right)\)
cho \(I=\frac{1.3+2}{4}.\frac{3.5+2}{16}.....\frac{\left(2^{2n}-1\right)\left(2^{2n}+1\right)+2}{2^{2n}}\)với n thuộc N. chứng minh \(I< \frac{4}{3}\)
Cho M=\(\frac{1.3+2}{4}.\frac{3.5+2}{16}.\frac{15.17+2}{256}.\frac{255.257+2}{65536}.....\frac{\left(2^{2n}-1\right)\left(2^{2n}+1\right)+2}{2^{2n}}\)
(n thuộc N)
Chứng minh M<\(\frac{4}{3}\)
17/lim\(\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2n-1\right)\left(2n+1\right)}\right)\)
18/lim\(\frac{1+a+a^2+...+a^n}{1+b+b^2+...+b^n}\left(\left|a\right|< 1;\left|b\right|< 1\right)\)
19/lim\(\frac{1-2+3-4+...+\left(2n-1\right)-2n}{2n+1}\)
Tìm số tự nhiên n, biết:
a)\(\frac{16}{2n}=2\)
b)\(\frac{\left(-3^n\right)}{81}=-27\)
1/ Tính:
a) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2\)
b) \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3\)
2/ Tìm số tự nhiên n, biết:
a) \(\frac{16}{2^n}=2\); b) \(\frac{\left(-3\right)^n}{81}=-27\); c) \(8^n:2^n=4\)
1.a.\(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2=\frac{17}{12}.\left(\frac{1}{20}\right)^2=\frac{17}{12}.\frac{1}{400}=\frac{17}{4800}\)
b. \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3=2\div\left(-\frac{1}{6}\right)^3=2\div\left(-\frac{1}{216}\right)=2.\left(-216\right)=-432\)
2.a.\(\frac{16}{2^n}=2\Rightarrow2^n=16:2=8=2^3\Rightarrow n=3\)
b.\(\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=-27.81=-2187=\left(-3\right)^7\Rightarrow n=7\)
c. \(8^n:2^n=4\Rightarrow\left(8:2\right)^n=4\Rightarrow4^n=4^1\Rightarrow n=1\)
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Tính
a) \(2\sqrt{\frac{25}{16}}-3\sqrt{\frac{49}{36}}+4\sqrt{\frac{81}{64}}\)
b) \(\left(3\sqrt{2}\right)^2-\left(4\sqrt{\frac{1}{2}}\right)^2+\frac{1}{16}.\left(\sqrt{\frac{3}{4}}\right)^2\)
c) \(\frac{2}{3}\sqrt{\frac{81}{16}}-\frac{3}{4}\sqrt{\frac{64}{9}}+\frac{7}{5}.\sqrt{\frac{25}{196}}\)
a) = \(\frac{7}{2}\)
b) = \(\frac{643}{64}\)
c) = 0
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Tìm số tự nhiên n biết:
a) \(\left[\left(0,5\right)^3\right]^n\)=\(\frac{1}{64}\)
b) \(\frac{64}{\left(-2\right)^{n+1}}=4\)
c) \(\left(\frac{1}{3}\right)^{n+1}=\frac{1}{81}\)
d) \(\left(\frac{3}{4}\right)^n.\frac{1}{2}=\frac{81}{512}\)
\(a,\left[\left(0,5\right)^3\right]^n=\frac{1}{64}\Rightarrow\left(0,125\right)^n=0,125^2\Rightarrow n=2\)
\(b,\frac{64}{\left(-2\right)^{n+1}}=4\Rightarrow\left(-2\right)^{n+1}=\frac{64}{4}\Rightarrow\left(-2\right)^{n+1}=16\Rightarrow\left(-2\right)^{n+1}=\left(-2\right)^4\)
\(\Rightarrow n+1=4\Rightarrow n=3\)
\(c,\left(\frac{1}{3}\right)^{n+1}=\frac{1}{81}\Rightarrow\left(\frac{1}{3}\right)^{n+1}=\left(\frac{1}{3}\right)^4\Rightarrow n+1=4\Rightarrow n=3\)
\(d,\left(\frac{3}{4}\right)^n.\frac{1}{2}=\frac{81}{512}\Rightarrow\left(\frac{3}{4}\right)^n=\frac{81}{512}:\frac{1}{2}=\frac{81}{256}\Rightarrow\left(\frac{3}{4}\right)^n=\left(\frac{3}{4}\right)^4\Rightarrow n=4\)
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