Rút gọn biểu thức sau
a/ \(^{3^{n+2}-3^{n+1}-6\cdot3^n}\)
b/(\(3\cdot2^{n-2}+2^n-2^n-2^{n-1}\)):5
Những câu hỏi liên quan
rút gọn \(B=\frac{5}{1\cdot2\cdot3}+\frac{5}{2\cdot3\cdot4}+....+\frac{5}{n\cdot\left(n+1\right)\left(n+2\right)}\)
\(B=\frac{5}{1.2.3}+\frac{5}{2.3.4}+...+\frac{5}{n.\left(n+1\right)\left(n+2\right)}\)
\(\Leftrightarrow\frac{2B}{5}=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{n\left(n+1\right)\left(n+2\right)}\)
\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{n\left(n+1\right)}-\frac{1}{\left(n+1\right)\left(n+2\right)}\)
\(=\frac{1}{2}-\frac{1}{\left(n+1\right)\left(n+2\right)}\)
\(\Rightarrow B=\frac{5}{4}-\frac{5}{2\left(n+1\right)\left(n+2\right)}\)
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a) Chứng minh 2010100+201099 chia hết cho 2011
b) Rút gọn biểu thức - dfrac{4^6cdot9^5+6^9cdot120}{8^4cdot3^{12}-6^{11}}
- dfrac{4^2cdot25^2+32cdot125}{2^3cdot5^2}
c) So sánh các lũy thừa
- 321 và 231
- 2300 và 3200
- 329 và 1813
d) Tìm số tự nhiên n biết: - dfrac{1}{9}cdot3^4cdot3^{n+1}9^4
- dfrac{1}{2}cdot2^n+4cdot2^n9cdot2^5
e) Chứng minh A và B là hai số tự nhiên liên tiếp
A20+21+22+23+...+220...
Đọc tiếp
a) Chứng minh 2010100+201099 chia hết cho 2011
b) Rút gọn biểu thức - \(\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
- \(\dfrac{4^2\cdot25^2+32\cdot125}{2^3\cdot5^2}\)
c) So sánh các lũy thừa
- 321 và 231
- 2300 và 3200
- 329 và 1813
d) Tìm số tự nhiên n biết: - \(\dfrac{1}{9}\cdot3^4\cdot3^{n+1}=9^4\)
- \(\dfrac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)
e) Chứng minh A và B là hai số tự nhiên liên tiếp
A=20+21+22+23+...+22011
a) \(2010^{100}+\)\(2010^{99}=2010^{99}.2010+2010^{99}.1=2010^{99}.\left(2010+1\right)=2010^{99}.2011\)Vậy biểu thức chia hết cho 2011.
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Tìm n∈Z, biết :
a) \(\frac{1}{9}\cdot27^n=3^n\)
b) \(3^{-2}\cdot3^4\cdot3^n=3^7\)
c) \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
d) \(32^{-n}\cdot16^n=2048\)
Lim frac{2^n+3^n}{3-4cdot3^{n+1}}
lim frac{4^{n+1}+10^n}{3^n-4cdot10^{n+1}}
lim frac{3^ncdot4^n-2^n}{12^n+5cdot3^{n+2}}
lim frac{left(-2right)^n+3^n}{left(-2right)^{n+1}-4cdot3^{n+1}+2}
lim frac{3^n-11}{1+7cdot2^{n+1}}
lim frac{2^n-3cdot5^n+1}{3cdot2^n+7cdot4^{n+1}}
Đọc tiếp
Lim \(\frac{2^n+3^n}{3-4\cdot3^{n+1}}\)
lim \(\frac{4^{n+1}+10^n}{3^n-4\cdot10^{n+1}}\)
lim \(\frac{3^n\cdot4^n-2^n}{12^n+5\cdot3^{n+2}}\)
lim \(\frac{\left(-2\right)^n+3^n}{\left(-2\right)^{n+1}-4\cdot3^{n+1}+2}\)
lim \(\frac{3^n-11}{1+7\cdot2^{n+1}}\)
lim \(\frac{2^n-3\cdot5^n+1}{3\cdot2^n+7\cdot4^{n+1}}\)
\(a=lim\frac{\left(\frac{2}{3}\right)^n+1}{3\left(\frac{1}{3}\right)^n-12}=-\frac{1}{12}\)
\(b=lim\frac{4\left(\frac{4}{10}\right)^n+1}{\left(\frac{3}{10}\right)^n-40}=-\frac{1}{40}\)
\(c=lim\frac{1-\left(\frac{2}{12}\right)^n}{1+45\left(\frac{3}{12}\right)^n}=\frac{1}{1}=1\)
\(d=\frac{\left(-\frac{2}{3}\right)^n+1}{-2\left(-\frac{2}{3}\right)^n-12+2\left(\frac{1}{3}\right)^n}=-\frac{1}{12}\)
\(e=\frac{1-11\left(\frac{1}{3}\right)^n}{\left(\frac{1}{3}\right)^n+14\left(\frac{2}{3}\right)^n}=\frac{1}{0}=+\infty\)
\(f=\frac{\left(\frac{2}{5}\right)^n-3+\left(\frac{1}{5}\right)^n}{3\left(\frac{2}{5}\right)^n+28\left(\frac{4}{5}\right)^n}=\frac{-3}{0}=-\infty\)
Rút gọn biểu thức : A= \(\frac{3}{\left(1\cdot2\right)^2}\) + \(\frac{5}{\left(2\cdot3\right)^2}\) + \(\frac{7}{\left(3\cdot4\right)^2}\) + .......+ \(\frac{2n+1}{\left[n\left(n+1\right)\right]^2}\)
A = \(\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+\frac{7}{\left(3.4\right)^2}+........+\frac{2n+1}{\left[n\left(n+1\right)\right]^2}\)
A = \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+............+\frac{2n+1}{2^2.\left(n+1\right)^2}\)
A = \(\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+........\frac{2n+1}{n^2.\left(n+1\right)^2}\)
A = \(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+.........+\frac{2n+1}{n^2}-\frac{2n+1}{\left(n+1\right)2}\)
A = \(\frac{1}{1}-\frac{2n+1}{\left(n+1\right)^2}\)
A = \(1-\frac{2n+1}{\left(n+1\right)2}\)
nha bạn.
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A=\(\frac{\left(2+1\right)1}{1^2.2^2}+\frac{\left(3+2\right)1}{2^2.3^2}+...+\frac{\left[\left(n+1\right)+n\right]1}{n^2\left(n+1\right)^2}\)
A=\(\frac{\left(2+1\right)\left(2-1\right)}{1^2.2^2}+\frac{\left(3+2\right)\left(3-2\right)}{2^2.3^3}+...+\frac{\left[\left(n+1\right)+n\right]\left[\left(n+1\right)-n\right]}{n^2\left(n+1\right)^2}\)
A=\(\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+...+\frac{\left(n+1\right)^2-n^2}{n^2.\left(n+1\right)^2}\)
A=\(\left(\frac{1}{1^2}-\frac{1}{2^2}\right)+\left(\frac{1}{2^2}-\frac{1}{3^2}\right)+...+\left(\frac{1}{n^2}-\frac{1}{\left(n+1\right)^2}\right)\)
A=1-\(\frac{1}{\left(n+1\right)^2}\)
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Xem thêm câu trả lời
Viết các biểu thức số sau dưới dạng an(a\(\in\)Q,n\(\in\)N)
a,\(9\cdot3^3\cdot\frac{1}{81}\cdot3^2\)
b,\(4\cdot2^5:\left(2^3\cdot\frac{1}{16}\right)\)
c,\(3^2\cdot2^5\cdot\left(\frac{2}{3}\right)^2\)
d,\(\left(\frac{1}{3}\right)^2\cdot\frac{1}{3}\cdot9^2\)
rút gọn \(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{\left(n-1\right)n}\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{\left(n-1\right)n}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n-1}-\frac{1}{n}\)
\(=1-\frac{1}{n}\)
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\(\frac{1}{\sqrt{1\cdot2}}+\frac{1}{\sqrt{2\cdot3}}+\frac{1}{\sqrt{3\cdot4}}+...+\frac{1}{\sqrt{n\cdot\left(n+1\right)}}\)
rút gọn phân thức
rút gọn biểu thức sau
a) -3(n-1)+4(2+n)
b) 4(n-2)-3(5-n)
c)7(8-n)+8(n-5)
d) -7(2n-1)-3(n-2)