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2 tháng 11 2019

Ai trả lời được k đúng luôn.

30 tháng 7 2018

a)\(4^{72}=\left(4^3\right)^{24}=64^{24}\)

\(8^{48}=\left(8^2\right)^{24}=64^{24}\)

\(\Rightarrow4^{72}=8^{48}\)

30 tháng 7 2018

a) \(4^{72}=\left(2^2\right)^{72}=2^{144}\)

\(8^{48}=\left(2^3\right)^{48}=2^{144}\)

mà \(2^{144}=2^{144}\)=> \(4^{72}=8^{48}\)

b) \(2^{252}=\left(2^2\right)^{126}=4^{126}\)

mà \(4^{126}< 5^{127}\)=> \(5^{127}>2^{252}\)

25 tháng 8 2020

a) \(B=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{302\cdot305}\)

\(B=\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{302\cdot305}\right)\)

\(B=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{302}-\frac{1}{305}\right)\)

\(B=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{305}\right)=\frac{1}{3}\cdot\frac{303}{610}=\frac{101}{610}\)

b) \(C=\frac{6}{1\cdot4}+\frac{6}{4\cdot7}+....+\frac{6}{202\cdot205}\)

\(C=2\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+...+\frac{3}{202\cdot205}\right)=2\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{202}-\frac{1}{205}\right)\)

\(=2\left(1-\frac{1}{205}\right)=2\cdot\frac{204}{205}=\frac{408}{205}\)

c) \(D=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+...+\frac{5^2}{266\cdot271}\)

\(D=5\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{266\cdot271}\right)\)

\(D=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{266}-\frac{1}{271}\right)=5\left(1-\frac{1}{271}\right)=5\cdot\frac{270}{271}=\frac{1350}{271}\)

d) \(E=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{5}{16}\cdot...\cdot\frac{9999}{10000}=\frac{3\cdot8\cdot15\cdot...\cdot9999}{4\cdot9\cdot16\cdot...\cdot10000}=\frac{3}{10000}\)

e) \(F=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{50^2}\right)\)

\(F=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{2500}\right)\)

\(F=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{2499}{2500}=\frac{3\cdot8\cdot15\cdot...\cdot2499}{4\cdot9\cdot16\cdot...\cdot2500}=\frac{3}{2500}\)

25 tháng 8 2020

a. \(B=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{302.305}\)

\(\Rightarrow3B=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{302.305}\)

\(\Rightarrow3B=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{302}-\frac{1}{305}\)

\(\Rightarrow3B=\frac{1}{2}-\frac{1}{305}\)

\(\Rightarrow3B=\frac{303}{610}\)

\(\Rightarrow B=\frac{101}{610}\)

b. \(C=\frac{6}{1.4}+\frac{6}{4.7}+...+\frac{6}{202.205}\)

\(\Rightarrow\frac{1}{2}C=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{202.205}\)

\(\Rightarrow\frac{1}{2}C=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{202}-\frac{1}{205}\)

\(\Rightarrow\frac{1}{2}C=1-\frac{1}{205}\)

\(\Rightarrow\frac{1}{2}C=\frac{204}{205}\)

\(\Rightarrow C=\frac{408}{205}\)

c. \(D=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{266.271}\)

\(\Rightarrow\frac{1}{5}D=\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{266.271}\)

\(\Rightarrow\frac{1}{5}D=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{266}-\frac{1}{271}\)

\(\Rightarrow\frac{1}{5}D=1-\frac{1}{271}\)

\(\Rightarrow\frac{1}{5}D=\frac{270}{271}\)

\(\Rightarrow D=\frac{1350}{271}\)

30 tháng 8 2020

a) \(\frac{21}{52}=\frac{210}{520}=1-\frac{310}{520}\)

\(\frac{213}{523}=1-\frac{310}{523}\)

Vì \(520< 523\)\(\Rightarrow\frac{1}{520}>\frac{1}{523}\)\(\Rightarrow\frac{310}{520}>\frac{310}{523}\)

\(\Rightarrow1-\frac{310}{520}< 1-\frac{310}{523}\)

hay \(\frac{21}{52}< \frac{213}{523}\)

b) \(\frac{1515}{9797}=\frac{15.101}{97.101}=\frac{15}{97}\)\(\frac{171171}{991991}=\frac{171.1001}{991.1001}=\frac{171}{991}\)

Ta có: \(\frac{15}{97}=\frac{150}{970}=1-\frac{820}{970}\)\(\frac{171}{991}=1-\frac{820}{991}\)

Vì \(970< 991\)\(\Rightarrow\frac{1}{970}>\frac{1}{991}\)\(\Rightarrow\frac{820}{970}>\frac{820}{991}\)

\(\Rightarrow1-\frac{820}{970}< 1-\frac{920}{991}\)

hay \(\frac{1515}{9797}< \frac{171171}{991991}\)

c) \(\frac{n+2}{n+3}=1-\frac{1}{n+3}\)\(\frac{n+3}{n+4}=1-\frac{1}{n+4}\)

Vì \(n\inℕ^∗\)\(\Rightarrow n+3< n+4\)\(\Rightarrow\frac{1}{n+3}>\frac{1}{n+4}\)

\(\Rightarrow1-\frac{1}{n+3}< 1-\frac{1}{n+4}\)

hay \(\frac{n+2}{n+3}< \frac{n+3}{n+4}\)

30 tháng 8 2020

d) \(\frac{n+7}{n+6}=1+\frac{1}{n+6}\)\(\frac{n+1}{n}=1+\frac{1}{n}\)

Vì \(n\inℕ^∗\)\(\Rightarrow n+6>n\)\(\Rightarrow\frac{1}{n+6}< \frac{1}{n}\)

\(\Rightarrow1+\frac{1}{n+6}< 1+\frac{1}{n}\)

hay \(\frac{n+7}{n+6}< \frac{n+1}{n}\)

8 tháng 2 2021

1) Ta có: \(\frac{2019}{2020}+\frac{2020}{2021}=\frac{2019}{2020}+\frac{4040}{4042}>\frac{4040}{4042}>\frac{4039}{4041}\)

Mà \(\frac{2019+2020}{2020+2021}=\frac{4039}{4041}\)

\(\Rightarrow\frac{2019}{2020}+\frac{2020}{2021}>\frac{2019+2020}{2020+2021}\)

2) BĐT cần CM tương đương:

\(\frac{a^2+b^2}{ab}\ge2\Leftrightarrow a^2+b^2\ge2ab\Leftrightarrow\left(a-b\right)^2\ge0\) (Luôn đúng)

Dấu "=" xảy ra khi: a = b

Hoặc có thể sử dụng BĐT Cauchy nếu bạn học cao hơn

8 tháng 2 2021

Tìm x e Z biết: 2x+1 e Ư (x+5) và x e N

giải giúp mình nhé!

mình cần gấpppppppppppppp

a,-3/5.2/7+-3/7.3/5+-3/7

=-3/7.2/5+(-3/7).3/5+(-3/7) 

=-3/7(2/5+3/5+1)

=-3/7.2

=-6/7

26 tháng 7 2018

Nhanh tay lên mk k cho , hôm nay mk có chuyện vui lên hào phóng tí!

26 tháng 7 2018

1,

\(\left(\frac{4}{9}-\frac{3}{7}-\frac{4}{11}\right)-\left(\frac{11}{7}+\frac{4}{9}-\frac{48}{11}\right)\)

\(=\frac{4}{9}-\frac{3}{7}-\frac{4}{11}-\frac{11}{7}-\frac{4}{9}+\frac{48}{11}\)

\(=\left(\frac{4}{9}-\frac{4}{9}\right)-\left(\frac{3}{7}+\frac{11}{7}\right)+\left(\frac{48}{11}-\frac{4}{11}\right)\)

\(=0-2+4\)

\(=2\)

2,

a, \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2018}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{2019}{2018}\)

\(=\frac{2019}{2}\)

b, \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2018}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2017}{2018}\)

\(=\frac{1}{2018}\)