B=1-1/4+1/4-1/7+1/7-1/10+...+1/27-1/30. =>B=1-1/30=29/30.
=1/1-1/4+1/4-1/7+1/7-1/10+...+1/27-1/30
=1/1-(1/4-1/4)-(1/7-1/7)-(1/10-1/10)-...-(1/27-1/27)-1/30
=1-0-0-0-...-0-1/30
=1-1/30
=1/29
Bạn tự kết luận nhé..!
\(B=\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{27\times30}\)
\(B=\frac{4-1}{1\times4}+\frac{7-4}{4\times7}+\frac{10-7}{7\times10}+...+\frac{30-27}{27\times30}\)
\(B=\frac{4}{1\times4}-\frac{1}{1\times4}+\frac{7}{4\times7}-\frac{4}{4\times7}+\frac{10}{7\times10}-\frac{7}{7\times10}+...+\frac{30}{27\times30}-\frac{27}{27\times30}\)
\(B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{27}-\frac{1}{30}\)
\(B=1-\frac{1}{30}\)
\(B=\frac{29}{30}\)
Vậy \(B=\frac{29}{30}\)
