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ở câu 1 ở mỗi phẫn số chúng ta cộng thêm 1, tổng là ta cộng thêm 5. Lấy 5 + -5=0. Rồi ta được tất cả tử là x+200,đặt chung ra ngoài,từ đó tính x=-200
A = \(\frac{1}{3}-\frac{3}{4}-\frac{-3}{5}+\frac{1}{73}-\frac{1}{36}+\frac{1}{15}+\frac{-2}{9}\)
A = \(\left(\frac{1}{3}-\frac{2}{9}\right)-\left(\frac{3}{4}+\frac{1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{73}\)
A = \(\left(\frac{3-2}{9}\right)-\left(\frac{27+1}{36}\right)+\left(\frac{9+1}{15}\right)+\frac{1}{73}\)
A = \(\frac{1}{9}-\frac{7}{9}+\frac{6}{9}+\frac{1}{73}\)
A = \(0+\frac{1}{73}=\frac{1}{73}\)
Làm
B = 1/3 - 3/4 - (-3)/5 + 1/73 - 1/36 + 1/15 + -2/9
B = 1/3 -3/4 + 3/5 +1/73 - 1/36 + 1/15 -2/9
B = [ 1/3 + 3/5 + 1/15 ] + [ -3/4 - 1/36 -2/9] + 1/73
B = [ 5/15 + 9/15 + 1/15 ] + [ -27/36 - 8/36 - 1/36 ] + 1/73
B = 1 + (-1) + 1/73
B = 1/73
HỌC TỐT Ạ
đặt \(A=\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+........+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)
\(\frac{1}{2}A=\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+........+\frac{1}{x.\left(x+1\right)}=\frac{2}{9}.\frac{1}{2}\)
\(\frac{1}{2}A=\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+........+\frac{1}{x.\left(x+1\right)}=\frac{1}{9}\)
\(\frac{1}{2}A=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+.....+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)
\(\frac{1}{2}A=\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{18}\)
\(\Rightarrow x+1=18\)
\(\Rightarrow x=18-1\)
\(\Rightarrow x=17\)
vậy \(x=17\)
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+....+\frac{1}{97.100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{97}-\frac{1}{100}\right)=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\left(1-\frac{1}{100}\right)=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{1}{3}\cdot\frac{99}{100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow\frac{33}{100}=\frac{0,33.x}{2009}\)
\(\Leftrightarrow x=\frac{0,33\times100}{0,33}=100\)
\(\frac{2}{20}+\frac{2}{30}+...+\frac{2}{Xx\left(X+1\right)}=\frac{2}{5}\)
2 . \(\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{Xx\left(X+1\right)}\right)=\frac{2}{5}\)
\(\frac{1}{4.5}+\frac{1}{5.6}+..+\frac{1}{Xx\left(X+1\right)}=\frac{2}{5}:2=\frac{1}{5}\)
\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{5}\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{1}{5}\)
\(\frac{1}{x+1}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}\)
=> x + 1 = 20
=> x = 19
\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{5}\)
\(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{5}\)
\(2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{5}\)
\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}:2\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{1}{5}\)
\(\frac{1}{x+1}=\frac{1}{4}-\frac{1}{5}=\frac{1}{20}\)
=> x + 1 = 20
=> x = 20 - 1
=> x = 19