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14 tháng 2 2016

Các bạn giải giùm mình nhanh nhanh được k? Mình đang cần gấp

25 tháng 4 2017

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)

\(2A=1-\frac{1}{3^{100}}\)

\(A=\frac{1-\frac{1}{3^{100}}}{2}\)

\(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(3B=\frac{5.3}{4.7}+\frac{5.3}{7.10}+\frac{5.3}{10.13}+...+\frac{5.3}{25.28}\)

\(3B=5\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

\(3B=5\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(3B=5\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(3B=5\cdot\frac{3}{14}=\frac{15}{14}\)

\(B=\frac{15}{14}:3=\frac{5}{14}\)

25 tháng 4 2017

a) \(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

\(3A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\right)\)

\(2A=1-\frac{1}{3^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)

b)  \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(B=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(B=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+...+\frac{5}{25.28}\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{5}{3}.\left(\frac{1}{7}-\frac{1}{10}\right)+\frac{5}{3}.\left(\frac{1}{10}-\frac{1}{13}\right)+...+\frac{5}{3}.\left(\frac{1}{25}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(B=\frac{5}{3}.\frac{3}{14}\)

\(\Rightarrow B=\frac{5}{14}\)

4 tháng 6 2019

1.

A= 5/28 + 5/70 +.....+10/700 = 5/(4.7)+5/(7.10)+....5/(25.28) 

3A= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28) 

3A= 5 (1/4-1/28) 

3A=15/14 

A= 5/14 

4 tháng 6 2019

#)Giải :

1. \(A=\frac{10}{54}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

\(A=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)

\(\Rightarrow\frac{3A}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)

\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)

\(\Rightarrow\frac{3A}{5}=\frac{1}{4}-\frac{1}{28}=\frac{3}{14}\)

\(\Rightarrow A=\frac{3}{14}\times\frac{5}{3}\)

\(\Rightarrow A=\frac{5}{14}\)

25 tháng 3 2017

\(A=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\\ A=\frac{1}{75}\)

\(B=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146+150}=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{94}+\frac{15}{94}-\frac{15}{98}+...+\frac{15}{146}-\frac{15}{150}\right)\)

\(B=\frac{1}{4}\left(\frac{15}{90}-\frac{15}{150}\right)=\frac{1}{60}\)

2 tháng 7 2017

Sorry đăng làm giwor thì em nó bấm nộp bài mk làm tiếp nhé 

\(E=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+......+\frac{1}{1+2+3+.....+24}\)

\(=\frac{1}{\frac{\left(2-1\right).2}{2}}+\frac{1}{\frac{\left(3-1\right).3}{2}}+.....+\frac{1}{\frac{\left(24-1\right).24}{2}}\)

\(=\frac{1}{\frac{1.2}{2}}+\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+.....+\frac{1}{\frac{23.24}{2}}\)

\(=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+.....+\frac{2}{23.24}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{23.24}\right)\)

\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{23}-\frac{1}{24}\right)\)

\(=2\left(1-\frac{1}{24}\right)\)

\(=2.\frac{23}{24}=\frac{23}{12}\)

Vậy tỉ số giữa D và E là ; \(\frac{5}{28}:\frac{23}{2}=\frac{5}{322}\)

2 tháng 7 2017

Ta có : \(D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+.....+\frac{10}{1400}\)

\(=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+.....+\frac{5}{25.28}\)

\(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+.....+\frac{3}{25.28}\right)\)

\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)\)

\(=\frac{5}{3}.\frac{3}{28}=\frac{5}{28}\)

5 tháng 2 2022

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@py. Hello, hihi