\(A=\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}=>\frac{1}{2}A=\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{304}\)
\(=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{16.19}=\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{16.19}\right)=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{16}-\frac{1}{19}\right)=\frac{1}{3}.\left(1-\frac{1}{19}\right)=\frac{1}{3}.\frac{18}{19}=\frac{6}{19}\)=> A= \(\frac{6}{19}:\frac{1}{2}=\frac{12}{19}\)
đúng nha
A=2/4+2/28+2/70+2/130+2/208+2/304
A=2/1.4+2/4.7+2/7.10+2/10.13+2/13.16+2/16.19
A=2/3.(1-1/4+1/4-1/7+...+1/16-1/19)
A=2/3.(1-1/19)
A=2/3.18/19
A=12/19
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