Question

A=\(\frac{15}{1\cdot6}\)+\(\frac{15}{6\cdot11}\)+\(\frac{15}{11\cdot16}\)+..+\(\frac{15}{2011\cdot2016}\)

so sánh Avới 3

giúp mik với mik cmar ơn nhiều

Answer 1

\(A=\frac{15}{1.6}+\frac{15}{6.11}+\frac{15}{11.16}+...+\frac{15}{2011.2016}\)

\(\Rightarrow\)\(\frac{1}{3}A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+..+\frac{5}{2011.2016}\)

\(\Rightarrow\)\(\frac{1}{3}A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2011}-\frac{1}{2016}\)

\(\Rightarrow\)\(\frac{1}{3}A=1-\frac{1}{2016}\)

\(\Rightarrow\)\(\frac{1}{3}A=\frac{2015}{2016}\)

\(\Rightarrow\)\(A=\frac{2015}{672}\)             (1)

Mà \(3=\frac{2016}{672}\)        (2)

Từ (1) và (2) suy ra A < 3