Question

[buianhquan]

\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+.........+\frac{1}{46.51}\)

Answer 1

[Arima Kousei]

\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{46.51}\)

\(=\frac{1}{5}.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{46.51}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{46}-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\left(1-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\left(\frac{51}{51}-\frac{1}{51}\right)\)

\(=\frac{1}{5}.\frac{50}{51}\)

\(=\frac{10}{51}\)

Chúc bạn học tốt !!! 

Answer 2

[Top 10 Gunny]

=1/5.(1-1/51)

=1/5.50/51

=10/51