Tìm \(n\in N\) biết \(3^{-1}\cdot3^n+5\cdot3^{n+1}=162\)
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Tìm n biết:
\(3^{-1}\cdot3^n+6\cdot3^{n-1}=7\cdot3^6\)
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vào đây nha https://coccoc.com/search/math#query=+3%5E%E2%88%921%C2%B73%5En%2B6%C2%B73%5En%E2%88%921%3D7%C2%B736++
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\(3^{-1}\cdot3^n+6\cdot3^{n-1}=7\cdot3^6\)
\(3^{n-1}+6\cdot3^{n-1}=7\cdot3^6\)
\(3^{n-1}\left(1+6\right)=7\cdot3^6\)
\(3^{n-1}\cdot7=7\cdot3^6\)
\(\Rightarrow3^{n-1}=3^6\)
\(\Rightarrow n-1=6\)
\(n=6+1=7\)
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\(3^{-1}.3^n+6.3^{n-1}=7.3^6\)
\(\Leftrightarrow\)\(3^{n-1}.6=7.3^6\)
Tới đây bạn tự giải đi nhé.
P/s: Thi thì bạn phải tự giải nhé, bài dễ như vậy mà bạn cũng lười động não thì đắp mềm ngủ cho rồi
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Xem thêm câu trả lời
Tìm n, biết:
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{n\cdot\left(n+1\right)\cdot\left(n+2\right)}>0,24995\)
\(3^{-1}\cdot3^n+6\cdot3^{n-1}=7\cdot3^6\)
Xét vế trái :\(3^{-1}.3^n+6.3^{n-1}=\frac{1}{3}.3^n+6.3^{n-1}=3^{n-1}+6.3^{n-1}=7.3^{n-1}\)
So sánh với vế phải , suy ra \(3^{n-1}=3^6\Leftrightarrow n-1=6\Leftrightarrow n=7\)
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1: \(\dfrac{\left(2^{12}\cdot3^5-4^6\cdot9^2\right)}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\dfrac{\left(5^{10}\cdot7^3-25^5\cdot49^2\right)}{\left(125\cdot7\right)^3-5^9\cdot14^3}\)
2: Chứng Minh với \(\forall N\in Z\) thì B= \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)
2:
\(B=3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n\cdot9+3^n-2^n\cdot4-2^n\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10⋮10\)
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Số tự nhiên n thỏa mãn: \(3^{n-1}+9\cdot3^n=28\cdot3^5\)là:
\(3^{n-1}+9.3^n=28.3^5\)
\(\Rightarrow3^{n-1}+9.3^{n-1}.3=28.3^5\)
\(\Rightarrow3^{n-1}.\left(1+9.3\right)=28.3^5\)
\(\Rightarrow3^{n-1}.28=28.3^5\)
\(\Rightarrow3^{n-1}=3^5\)
\(\Rightarrow n-1=5\)
\(\Rightarrow n=6\)
Vậy n = 6
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mấy bài này để để mấy bạn khác làm,HUY TƯ là cộng tác viên nên làm những bài khó hơn
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tìm tất cả các số nguyên n thỏa mãn các đẳng thức sau
\(5^3\cdot25^n=5^{3n}\)
\(a^{\left(2n+6\right)\cdot\left(3n-9\right)}=1\)
\(\dfrac{1}{3}\cdot3^n=7\cdot3^2\cdot9^2-2\cdot3^n\)
a: \(5^3\cdot25^n=5^{3n}\)
\(\Leftrightarrow5^{3n}=5^3\cdot5^{2n}\)
=>3n=2n+3
hay n=3
b: \(a^{\left(2n+6\right)\left(3n-9\right)}=1\)
=>(2n+6)(3n-9)=0
=>n=-3 hoặc n=3
c: \(\dfrac{1}{3}\cdot3^n=7\cdot3^2\cdot3^4-2\cdot3^n\)
\(\Leftrightarrow3^n\cdot\dfrac{1}{3}+3^n\cdot2=7\cdot3^6\)
\(\Leftrightarrow3^n=3^7\)
hay n=7
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Tính tổng :a) Afrac{5}{2cdot1}+frac{4}{1cdot11}+frac{3}{11cdot14}+frac{1}{14cdot15}+frac{13}{15cdot28}b) Bfrac{-1}{20}+frac{-1}{30}+frac{-1}{42}+frac{-1}{56}+frac{-1}{72}+frac{-1}{90}c) Cfrac{1}{1cdot2cdot3}+frac{1}{2cdot3cdot4}+...+frac{1}{nleft(n+1right)left(n+2right)}d) Dfrac{1}{1cdot2cdot3cdot4}+frac{1}{2cdot3cdot4cdot5}+...+frac{1}{nleft(n+1right)left(n+2right)left(n+3right)}e) Eleft(frac{1}{1cdot2cdot3}+frac{1}{2cdot3cdot4}+...+frac{1}{37cdot38cdot39}right)cdot1482cdot185cdot8
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Tính tổng :
a) \(A=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot14}+\frac{1}{14\cdot15}+\frac{13}{15\cdot28}\)
b) \(B=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
c) \(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
d) \(D=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}\)
e) \(E=\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\cdot1482\cdot185\cdot8\)
Tính tổng :
a) Afrac{5}{2cdot1}+frac{4}{1cdot11}+frac{3}{11cdot14}+frac{1}{14cdot15}+frac{13}{15cdot28}
b) Bfrac{-1}{20}+frac{-1}{30}+frac{-1}{42}+frac{-1}{56}+frac{-1}{72}+frac{-1}{90}
c) Cfrac{1}{1cdot2cdot3}+frac{1}{2cdot3cdot4}+...+frac{1}{nleft(n+1right)left(n+2right)}
d) Dfrac{1}{1cdot2cdot3cdot4}+frac{1}{2cdot3cdot4cdot5}+...+frac{1}{nleft(n+1right)left(n+2right)left(n+3right)}
e) Eleft(frac{1}{1cdot2cdot3}+frac{1}{2cdot3cdot4}+...+frac{1}{37cdot38cdot39}right)cdot1482cdot185cdot8
Đọc tiếp
Tính tổng :
a) \(A=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot14}+\frac{1}{14\cdot15}+\frac{13}{15\cdot28}\)
b) \(B=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)
c) \(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
d) \(D=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}\)
e) \(E=\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{37\cdot38\cdot39}\right)\cdot1482\cdot185\cdot8\)
\(A=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(\frac{A}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)
\(\frac{A}{7}=\frac{7-2}{2.7}+\frac{11-7}{7.11}+\frac{14-11}{11.4}+\frac{15-14}{14.15}+\frac{28-15}{15.28}\)
\(\frac{A}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)
\(A=7.\frac{13}{28}\)
\(A=\frac{13}{4}\)
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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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