\(\frac{13}{4}\)

\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(\Rightarrow\frac{B}{7}=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)

\(\Rightarrow\frac{B}{7}=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)

\(\Rightarrow\frac{B}{7}=\frac{1}{2}-\frac{1}{28}\)

\(\Rightarrow\frac{B}{7}=\frac{14}{28}-\frac{1}{28}\)

\(\Rightarrow\frac{B}{7}=\frac{13}{28}\)

\(\Rightarrow B=\frac{13}{28}.7\)

\(\Rightarrow B=\frac{13}{4}\)

Trả lời:

\(\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}\)\(+\frac{13}{15\cdot4}\)

\(=\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}\)\(+\frac{13}{60}\)

\(=\frac{55+8+3}{22}\)\(+\frac{2+13}{60}\)

\(=\frac{66}{22}\)\(+\frac{1}{4}\)

\(=\frac{13}{4}\)

Hc tốt #

\(B=\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)

\(\dfrac{B}{7}=\dfrac{5}{2.7}+\dfrac{4}{7.11}+\dfrac{3}{11.14}+\dfrac{1}{14.15}+\dfrac{13}{15.4}\)

\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{7}{11}+...+\dfrac{1}{15}-\dfrac{1}{28}\)

\(\dfrac{B}{7}=\dfrac{1}{2}-\dfrac{1}{28}\)

\(\dfrac{B}{7}=\dfrac{13}{28}\)

\(B=\dfrac{13}{28}.7=\dfrac{13}{4}\)

\(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{2}{2.15}+\frac{13}{15.4}\)

\(B=\frac{1}{2}-1+1-\frac{1}{11}+\frac{1}{11}-\frac{1}{2}+\frac{1}{2}-\frac{1}{15}+\frac{1}{15}-\frac{1}{4}\)

\(B=\frac{1}{2}-\frac{1}{4}\)

\(B=\frac{1}{4}\)

đáp án là:1/4
 

B= 13 phan 4