Question

5 mũ 2 phần 1*6 + 5 mũ 2 phần 6*11 +...+5 mũ 2 phần 26*31

Answer 1

ĐẶT \(A=....\)

\(\Rightarrow5A=\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{26\cdot31}=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-...+\frac{1}{26}-\frac{1}{31}\)

\(\Rightarrow5A=1-\frac{1}{31}=\frac{30}{31}\Rightarrow A=\frac{30}{155}=\frac{6}{31}\)

Answer 2

Đặt A = ...

\(\Rightarrow A=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)

\(\Rightarrow A=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(\Rightarrow A=5.\left(1-\frac{1}{31}\right)\)

\(\Rightarrow A=5.\frac{30}{31}\)

\(\Rightarrow A=\frac{150}{31}\)

Answer 3

Đặt \(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+..+\frac{5^2}{26.31}\)

\(\Leftrightarrow S=\frac{25}{1.6}+\frac{25}{6.11}+..+\frac{25}{26.31}\)

\(\Leftrightarrow\frac{1}{5}S=\frac{5}{1.6}+\frac{5}{6.11}+..+\frac{5}{26.31}\)

\(\Leftrightarrow\frac{1}{5}S=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+..+\frac{1}{26}-\frac{1}{31}\)

\(\Leftrightarrow\frac{1}{5}S=1-\frac{1}{31}\)

\(\Leftrightarrow\frac{1}{5}S=\frac{30}{31}\)

\(\Leftrightarrow S=\frac{30}{31}\div\frac{1}{5}\)

\(\Leftrightarrow S=\frac{150}{31}\)