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2 tháng 4 2018

\(P=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+\frac{4}{5^5}+...+\frac{11}{5^{12}}\)

\(\Rightarrow\)\(5P=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+...+\frac{11}{5^{11}}\)

\(\Rightarrow\)\(4P=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}+...+\frac{1}{5^{11}}-\frac{1}{5^{12}}\)

\(\Rightarrow\)\(20P=1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{10}}-\frac{1}{5^{11}}\)

\(\Rightarrow\)\(16P=1-\frac{1}{5^{11}}+\frac{1}{5^{12}}-\frac{1}{5^{11}}\)\(< 1\)

\(\Rightarrow\)\(P< \frac{1}{16}\)

P/s: nguyên tác: https://olm.vn/thanhvien/nhatphuonghocgiot

16 tháng 8 2018

Đạt BD

11 tháng 8 2016

\(B=\frac{1}{5}-\frac{3}{7}+\frac{5}{9}-\frac{2}{11}+\frac{7}{13}-\frac{9}{16}-\frac{7}{13}+\frac{2}{12}-\frac{5}{9}+\frac{3}{7}-\frac{1}{5}-\frac{1}{5}\)

\(B=\left(\frac{1}{5}-\frac{1}{5}\right)-\left(\frac{3}{7}-\frac{3}{7}\right)+\left(\frac{5}{9}-\frac{5}{9}\right)+\left(\frac{7}{13}-\frac{7}{13}\right)-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

\(B=0-0+0+0-\frac{2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

\(B=\frac{-2}{11}+\frac{2}{12}-\frac{9}{16}-\frac{1}{5}\)

Đến đây chỉ còn cách quy đồng thôi

24 tháng 10 2021

qwertyuiopasdfgggggghjkllzxcvbnmm,.//234567890-=`

24 tháng 10 2021
Chịu khó đọc lại đi dễ mà
18 tháng 4 2018

\(A=\frac{\left(23\frac{11}{15}-26\frac{13}{20}\right)}{12^2+5^2}\cdot\frac{1-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}}{3^2.13.2-13.5}-\frac{19}{37}\)

\(A=\frac{\left(23+\frac{11}{15}-26+\frac{13}{20}\right)}{144+25}\cdot\frac{1-\frac{1}{5.6}-\frac{1}{6.7}-\frac{1}{7.8}}{9.13.2-13.5}-\frac{19}{37}\)

\(A=\frac{\left(23+26+\frac{11}{15}-\frac{13}{20}\right)}{169}\cdot\frac{1-\left(\frac{1}{5}-\frac{1}{6}\right)-\left(\frac{1}{6}-\frac{1}{7}\right)-\left(\frac{1}{7}-\frac{1}{8}\right)}{13.\left(9.2-5\right)}-\frac{19}{37}\)

\(A=\frac{49+\frac{44}{60}-\frac{39}{60}}{169}\cdot\frac{1-\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+\frac{1}{8}}{13.13}-\frac{19}{37}\)

\(A=\frac{49+\frac{1}{20}}{169}\cdot\frac{1-\frac{1}{5}+\frac{1}{8}}{169}-\frac{19}{37}\)

\(A=\frac{49\frac{1}{20}}{169}\cdot\frac{\frac{4}{5}+\frac{5}{40}}{169}-\frac{19}{37}\)

\(A=\frac{981}{169}\cdot\frac{\frac{32}{40}+\frac{5}{40}}{169}-\frac{19}{37}\)

\(A=\frac{981}{169}\cdot\frac{\frac{37}{40}}{169}-\frac{19}{37}\)

\(A=\frac{981.\frac{37}{40}}{169^2}-\frac{19}{37}\)

\(A=\frac{\frac{36297}{40}}{28561}-\frac{19}{37}\)

\(A=\frac{907,425}{28561}-\frac{19}{37}\)

\(A=\frac{33574,725}{1056757}-\frac{542659}{1056757}\)

\(A=\frac{-509084,275}{1056757}=-0,04604282...\)

Mik chỉ làm đc thế này thôi, ôn thi học kì II tốt nha bạn!

10 tháng 8 2018

a)  \(\left(\frac{2}{5}-\frac{1}{2}\right)^2-\frac{11}{5}:\frac{-11}{5}=\left(-\frac{1}{10}\right)^2+1=1\frac{1}{100}\)

b)  \(\left(-\frac{5}{7}\right)^2+8.\left(0,5\right)^2+\left(-1\right)^{2010}=\frac{25}{49}+2+1=3\frac{25}{49}\)

c)  \(\frac{9999^2}{3333^2}+\left(0,5\right)^2.\left(-2\right)^4-\left(-\frac{4}{3}\right)^2=9+1-\frac{16}{9}=8\frac{2}{9}\)

d) \(\left|-\frac{2}{5}+\frac{1}{7}\right|:\frac{-3}{35}+\frac{-3}{7}.\frac{7}{5}=\frac{9}{35}.\frac{35}{-3}-\frac{3}{5}=-3\frac{3}{5}\)

e) \(\frac{1}{2}-\left(-0,4\right)+\frac{1}{3}+\frac{1}{5}-\frac{-1}{6}+\frac{-4}{35}+\frac{1}{41}\)

\(=\frac{1}{2}+\frac{2}{5}+\frac{1}{3}+\frac{1}{5}+\frac{1}{6}-\frac{4}{35}+\frac{1}{41}=1\frac{732}{1435}\)

23 tháng 9 2017

1) \(\left|x-\frac{3}{5}\right|< \frac{1}{3}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{3}{5}< \frac{1}{3}\\x-\frac{3}{5}< -\frac{1}{3}\end{cases}}\Rightarrow\orbr{\begin{cases}x< \frac{1}{3}+\frac{3}{5}\\x< \frac{-1}{3}+\frac{3}{5}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x< \frac{5}{15}+\frac{9}{15}\\x< \frac{-5}{15}+\frac{9}{15}\end{cases}}\Rightarrow\orbr{\begin{cases}x< \frac{14}{15}\\x< \frac{4}{15}\end{cases}}\)

                vay \(\orbr{\begin{cases}x< \frac{14}{15}\\x< \frac{4}{15}\end{cases}}\)

2) \(\left|x+\frac{11}{2}\right|>\left|-5,5\right|\)

\(\left|x+\frac{11}{2}\right|>5,5\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{11}{2}>\frac{11}{2}\\x+\frac{11}{2}>-\frac{11}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x>\frac{11}{2}-\frac{11}{2}\\x>\frac{-11}{2}-\frac{11}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>0\\x>-11\end{cases}}\)

vay \(\orbr{\begin{cases}x>0\\x>-11\end{cases}}\)

3) \(\frac{2}{5}< \left|x-\frac{7}{5}\right|< \frac{3}{5}\)

\(\Rightarrow\left|x-\frac{7}{5}\right|>\frac{2}{5}\) va \(\left|x-\frac{7}{5}\right|< \frac{3}{5}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{7}{5}>\frac{2}{5}\\x-\frac{7}{5}>\frac{-2}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x>\frac{2}{5}+\frac{7}{5}\\x>\frac{-2}{5}+\frac{7}{5}\end{cases}}\)va \(\orbr{\begin{cases}x-\frac{7}{5}< \frac{3}{5}\\x-\frac{7}{5}< \frac{-3}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x< \frac{3}{5}+\frac{7}{5}\\x< \frac{-3}{5}+\frac{7}{5}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>\frac{9}{5}\\x>1\end{cases}}\)va \(\orbr{\begin{cases}x< 2\\x< \frac{4}{5}\end{cases}}\)

vay ....

1 tháng 8 2018

a, \(\frac{3}{8}+\frac{11}{13}-\frac{9}{13}\)

  =\(\frac{3}{8}+\frac{2}{13}\)

  =\(\frac{55}{104}.\)

b, \(\frac{2}{7}.\left(\frac{5}{9}+\frac{4}{9}\right)+\frac{2}{7}\)

  =\(\frac{2}{7}.\frac{9}{9}+\frac{2}{7}\)

  =\(\frac{2}{7}+\frac{2}{7}\)

  =\(\frac{4}{7}\)

c, \(\frac{3}{11}.\left(\frac{3}{5}-\frac{5}{3}\right)-\frac{3}{10}.\left(\frac{1}{3}-\frac{2}{5}\right)\)

  =\(\frac{3}{11}.-\frac{16}{15}-\frac{3}{10}.-\frac{1}{15}\)

  =\(-\frac{16}{55}--\frac{1}{50}\)

  =\(-\frac{149}{550}.\)

d, \(\frac{-3}{4}.\frac{11}{23}+\frac{3}{23}.\frac{31}{17}-\frac{3}{17}.\frac{19}{23}\)

  =\(-\frac{33}{92}+\frac{93}{391}-\frac{57}{391}\)

  =\(-\frac{417}{1564}\)

e, \(\frac{3}{17}.\frac{11}{23}+\frac{3}{23}.\frac{31}{17}-\frac{3}{17}.\frac{19}{23}\)

  =\(\frac{33}{391}+\frac{93}{391}--\frac{254}{391}\)

  =\(\frac{380}{391}.\)

g, \(\frac{3}{7}.\frac{-5}{12}+\frac{11}{17}:\frac{5}{-12}\)

  =\(-\frac{5}{28}+-\frac{132}{85}\)

  = \(-1.731512605.\)

k cho mình nha làm mỏi tay quá ,.....................kết bạn với mình nha.......................

5 tháng 8 2018

THANK  Ngô Bùi Hoa  làm cho mình bài 2 với