\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{96.101}\)
\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{96.101}\right)\)
\(S=5.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\right)\)
\(S=5.\left(\frac{1}{1}-\frac{1}{101}\right)\)
\(S=5.\left(\frac{101}{101}-\frac{1}{101}\right)\)
\(S=5.\frac{100}{101}\)
\(S=\frac{500}{101}\)
4/
a. Ta có:
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{96.101}=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{96.101}\right)=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{96}-\frac{1}{101}\right)=5.\left(1-\frac{1}{101}\right)=5.\frac{100}{101}=\frac{500}{101}\)
Vậy \(S=\frac{500}{101}\)
b.
Ta có:
9999.ab chia hết cho 11
99.ab chia hết cho 11
ab+cd+ef chia hết cho 11
=> 9999.ab+99.cd+(ab+cd+ef) chia hết cho 11
=>10000.ab+100.cd+ef chia hết cho 11
=> abcdef chia hết cho 11
( Bạn tự cho dấu gạch trên đầu nhá)