Question

Tính nhanh :

 Q= 5^2/1.6 +5^2 /6.11 +5^2/11.6 +...+5^2/26.31

Answer 1

\(Q=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)

\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)

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

\(=5\cdot\frac{30}{31}=\frac{150}{31}\)

Answer 2

Bạn nhân 2 lên rồi áp dụng \(\frac{5}{a\times\left(a+5\right)}=\frac{1}{a}-\frac{1}{a+5}\) thì sẽ còn lại là    2Q=1-1/31 =30/31 nên Q=30/62