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= 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
\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(=\frac{1}{1.3}-\frac{1}{11.13}\)
\(=\frac{1}{3}-\frac{1}{143}\)
\(=\frac{140}{429}\)
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)\(\frac{49+7.49}{49}\)=\(\frac{392}{49}\)=\(8\)
ta có: \(B=\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405}\)
\(=\frac{1}{2}.\left(\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{401.405}\right)\)
\(=\frac{1}{2}.\frac{1}{4}.\left(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{401.405}\right)\)
\(=\frac{1}{8}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{17}-...-\frac{1}{401}+\frac{1}{405}\right)\)
\(=\frac{1}{8}.\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(=\frac{1}{8}.\frac{80}{405}=\frac{10}{405}=\frac{2}{81}\)
A=\(2.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\right)\)
A=\(2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)
A=\(2.\left(1-\frac{1}{13}\right)\)
A=\(2.\frac{12}{13}=\frac{24}{13}\)
A=2(2/1.3+2/3.5+2/5.7+...+2/11.13)
A=2(1/1-1/3+1/3-1/5+1/5-1/7+...+1/11-1/13)
A=2(1/1-1/13)=2.12/13=24/13
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