\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(\frac{5^2}{1.6}=5.\left(\frac{1}{1}-\frac{1}{6}\right)\)
\(\frac{5^2}{6.11}=5.\left(\frac{1}{6}-\frac{1}{11}\right)\)
............................
\(\frac{5^2}{26.31}=5.\left(\frac{1}{26}-\frac{1}{31}\right)\)
cộng hết lại: \(5.\left(\frac{1}{1}-\frac{1}{31}\right)=5\left(\frac{30}{31}\right)=\frac{150}{31}\)
Ta có :
\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)
\(=\)\(5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)
\(=\)\(5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=\)\(5\left(1-\frac{1}{31}\right)\)
\(=\)\(5-\frac{5}{31}\)
\(=\)\(\frac{150}{31}\)
Chúc bạn học tốt ~
Ta có : 521.6+526.11+5211.16+...+5226.31521.6+526.11+5211.16+...+5226.31 ==5(51.6+56.11+511.16+...+526.31)5(51.6+56.11+511.16+...+526.31) ==5(11−16+16−111+111−116+...+126−131)5(11−16+16−111+111−116+...+126−131) ==5(1−131)5(1−131) ==5−5315−531 ==15031 |