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Áp dụng theo dạng toán số ai cập ta có:
4/1.5+4/5.9+4/9.13+4/13.17+4/17.21=1/1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21=1-1/21 < 1
Vậy tổng đó < 1
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}\)
\(=\frac{1}{3}-\frac{1}{143}\)
\(=\frac{140}{429}\)
Mình sửa lại đề bạn sai nhé\(G=\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+....+\frac{7}{21.25}\)
\(=\frac{7.4}{1.5.4}+\frac{7.4}{5.9.4}+\frac{7.4}{9.13.4}+....+\frac{7.4}{21.25.4}\)
\(=\frac{7}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{21.25}\right)\)
\(=\frac{7}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{21}-\frac{1}{25}\right)\)
\(=\frac{7}{4}.\left(1-\frac{1}{25}\right)\)
\(=\frac{7}{4}.\frac{24}{25}\)
\(\frac{42}{25}\)
2, tính vế trc
\(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{19.21}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{19}-\frac{1}{21}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{21}\right)=\frac{1}{2}.\frac{2}{7}=\frac{1}{7}\)
=> 1/7 . x = 9/7
x = 9/7 . 7
x = 9
a) \(\frac{4.7}{9.32}\)=\(\frac{28}{288}\)=\(\frac{7}{72}\)
b)\(\frac{3.21}{14.15}\)=\(\frac{63}{210}\)=\(\frac{3}{10}\)
c)\(\frac{2.5.13}{26.35}\)=\(\frac{130}{910}\)=\(\frac{1}{7}\)
d)\(\frac{9.6-9.3}{18}\)=\(\frac{27}{18}\)=\(\frac{3}{2}\)
e)\(\frac{17.5-17}{3-20}\)=\(\frac{68}{-17}\)=\(-4\)
f)\(\frac{49+7.49}{49}\)=\(\frac{392}{49}\)=\(8\)
=> 1/11 - 1/13 + 1/13 - 1/15 + ..... + 1/19 - 1/21 - x + 4 + 221/231 = 7/3
=> 1/11 - 1/21 - x + 4 + 221/231 = 7/3
=> 2099/420 - x = 7/3
=> x = 2099/420 - 7/3 = 373/140
Tk mk nha
Bài làm
\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2\left(\frac{1}{11}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow2.\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow\frac{20}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}+\frac{221}{231}=\frac{539}{231}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{539}{231}-\frac{221}{231}\)
\(\Leftrightarrow\frac{20}{231}-x+\frac{924}{231}=\frac{318}{231}\)
\(\Leftrightarrow\frac{20}{231}-x=\frac{318}{231}-\frac{924}{231}\)
\(\Leftrightarrow\frac{20}{231}-x=-\frac{606}{231}\)
\(\Leftrightarrow x=\frac{20}{231}-\frac{606}{231}\)
\(\Leftrightarrow x=-\frac{586}{231}\)
Vậy \(\Leftrightarrow=-\frac{586}{231}\)
\(a,\left(10\frac{2}{9}.2\frac{3}{5}\right)-6\frac{2}{9}=\frac{1196}{45}-\frac{56}{9}=\frac{1196}{45}-\frac{280}{45}=\frac{916}{45}\)
\(b,\frac{6}{7}+\frac{1}{7}.\frac{2}{7}+\frac{1}{7}.\frac{5}{7}=\frac{1}{7}\left(6+\frac{2}{7}+\frac{5}{7}\right)=\frac{1}{7}.7=1\)
\(c,3.136.8+4.14.6-14.150=3264+336-2100=1500\)
\(d,\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{10.11}\)\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)\(=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)
\(e,\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{37.39}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{37}-\frac{1}{39}=\frac{1}{3}-\frac{1}{39}=\frac{4}{13}\)
= 7/4.(4/1.5 + 4/5.9 + 4/9.13 + 4/13.17 + 4/17.21)
= 7/4.(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
= 7/4.(1-1/21)
= 7/4.20/21 = 5/3
Tk mk nha
Đặt biểu thức bằng A
4/7A=1-1/5+1/5-1/9+...+1/17_1/21
4/7A=1-1/21
4/7A=20/21
A=35/21=5/3