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\(E=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)
\(E=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{31.34}\right)\)
\(E=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)
\(E=\frac{2}{3}\left(1-\frac{1}{34}\right)\)
\(E=\frac{2}{3}.\frac{33}{34}\)
\(E=\frac{11}{17}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)
\(C=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{31.34}\right)\)
\(C=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)
\(C=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{34}\right)\)
\(C=\frac{2}{3}.\frac{33}{34}\)
\(C=\frac{11}{17}\)
\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)
\(=\frac{2}{3}\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{31.34}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{34}\right)=\frac{2}{3}.\frac{33}{34}=\frac{11}{17}\)
Gọi dãy trên là A
3/5A=3(4.7)+3/(7.10)+......+(3/(31+34)
=1/4-1/7+1/7-1/10+........+1/31-1/34
=1/4-1/34=15/68
\(=-\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{61}-\dfrac{1}{64}\right)=-\dfrac{1}{63}\)