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=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+............+\frac{1}{18.19.20}\)
=\(\frac{2}{1.2.3.2}+\frac{2}{2.3.4.2}+............+\frac{2}{18.19.20.2}\)
=\(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}............+\frac{1}{18.19}-\frac{1}{19.20}\)
=\(\frac{1}{1.2}-\frac{1}{19.20}\)
=\(\frac{189}{380}\)
\(F=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\)
\(\Rightarrow\)\(\frac{1}{2}F=\frac{1}{2}.\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\right)\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{380}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{19.20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{1}{5}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{4}{20}-\frac{1}{20}\)
\(\Rightarrow\) \(\frac{1}{2}F=\frac{3}{20}\)
\(\Rightarrow\)\(F=\frac{3}{20}\div\frac{1}{2}\)
\(\Rightarrow\) \(F=\frac{3}{20}.2\)
\(\Rightarrow\)\(F=\frac{3}{10}\)
\(F=\frac{1}{15}+\frac{ 1}{21}+...+\frac{1}{190}\)
\(F=\frac{2}{30}+\frac{2}{21}+...+\frac{2}{380}\)
\(F=\frac{2}{5.6}+...+\frac{2}{19.20}\)
\(F=2.\left(\frac{1}{5.6}+...+\frac{1}{19.20}\right)\)
\(F=2.\left(\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(F=2\left[\frac{1}{5}-\left(\frac{1}{6}-\frac{1}{6}\right)-...-\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{20}\right]\)
\(F=2.\left(\frac{1}{5}-\frac{1}{20}\right)\)
\(F=2.\frac{3}{20}\)
\(F=\frac{6}{20}=\frac{3}{10}\)
\(G=\frac{12}{84}+\frac{12}{210}+...+\frac{12}{2100}\)
\(G=\frac{4}{28}+\frac{4}{70}+...+\frac{4}{700}\)
\(G=\frac{4}{4.7}+\frac{4}{7.10}+...+\frac{4}{25.28}\)
\(G=\frac{4}{3}.\left(\frac{3}{4.7}+...+\frac{3}{25.28}\right)\)
\(G=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{7}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(G=\frac{4}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)\)
\(G=\frac{4}{3}.\frac{6}{28}\)
\(G=\frac{2}{7}\)
Tổng của G và F là : \(\frac{3}{10}+\frac{2}{7}=\frac{21}{70}+\frac{20}{70}=\frac{41}{70}\)
\(11M=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=\frac{11^6+1}{11^6+1}+\frac{10}{11^6+1}=1+\frac{10}{11^6+1}\)
\(11N=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=\frac{11^7+1}{11^7+1}+\frac{10}{11^7+1}=1+\frac{10}{11^7+1}\)
vì \(\frac{10}{11^6+1}>\frac{10}{11^7+1}\)
nên\(11M>11N\)
=>\(M>N\)
\(M=\frac{11^5+1}{11^6+1}\)
\(\Rightarrow11M=11.\frac{11^5+1}{11^6+1}=\frac{11^6+11}{11^6+1}=\frac{11^6+1+10}{11^6+1}=1+\frac{10}{11^6+1}\)
\(N=\frac{11^6+1}{11^7+1}\)
\(\Rightarrow11N=11.\frac{11^6+1}{11^7+1}=\frac{11^7+11}{11^7+1}=\frac{11^7+1+10}{11^7+1}=1+\frac{10}{11^7+1}\)
Do \(1+\frac{10}{11^6+1}>1+\frac{10}{11^7+1}\)
\(\Rightarrow11M>11N\)
\(\Rightarrow M>N\)
\(\frac{x}{9}-\frac{3}{y}=\frac{1}{18}\)
=> \(\frac{3}{Y}=\frac{X}{9}-\frac{1}{18}\)
=>\(\frac{3}{Y}=\frac{2X}{18}-\frac{1}{18}\)
=>\(\frac{3}{y}=\frac{2x-1}{18}\)
=> 54 = y(2x-1)
=> y(2x-1) là ước lẻ.
Ta có bảng sau
| y | 54 | 2 | 18 | 6 |
| 2x-1 | 1 | 27 | 3 | 9 |
| x | 0 | 14 | 2 | 5 |
\(\frac{x}{9}-\frac{3}{y}=\frac{1}{18}\\ 2xy-54=1\\ 2xy=55\\ xy=\frac{55}{2}\). Điều kiện của x, y là gì bạn ?, nếu ko có dk thì bài này ko làm được đâu
\(\frac{x+1}{3}=\frac{9}{2}\)
\(\left(x+1\right).2=9.3\)
\(\left(x+1\right).2=27\)
\(x+1=27:2\)
\(x+1=13,5\)
\(x=13,5-1=12,5\)
vậy x = 12.5
\(\frac{x+1}{3}=\frac{9}{2}\)
\(\Leftrightarrow2\left(x+1\right)=3\times9\)
\(\Leftrightarrow2\left(x+1\right)=27\)
\(\Leftrightarrow x+1=\frac{27}{2}\)
\(\Leftrightarrow x=\frac{25}{2}\)
Sửa đề nha :
\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{2015\cdot2017}\)
\(=\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2016}{2017}=\frac{1008}{2017}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2016.2017}\)
\(=\frac{1}{2}\left[\left[\frac{1}{1}-\frac{1}{3}\right]+\left[\frac{1}{3}-\frac{1}{5}\right]+...+\left[\frac{1}{2016}-\frac{1}{2017}\right]\right]\)
= \(=\frac{1}{2}\left[1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2016}-\frac{1}{2017}\right]\)
\(=\frac{1}{2}.\left[1-\frac{1}{2017}\right]\)
= 1/2. 2016 / 2017 = 1008/2017
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