Question

Bài 4: Tính hợp lý

A=\(\frac{4}{1\cdot2}+\frac{4}{3\cdot5}+.......+\frac{4}{20\cdot11\cdot2013}\)

Bài 5: So sánh với 1:

A=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{49\cdot50}\)

Answer 1

Bài 5:

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}< 1\)

Vậy A<1.

Bài 4: Bn ghi nhầm đề rồi.

Đề đúng: \(A=\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{2011.2013}\)

\(\frac{1}{2}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2011.2013}\)

\(\frac{1}{2}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\)

\(\frac{1}{2}A=1-\frac{1}{2013}\)

\(A=2.\frac{2012}{2013}=\frac{4024}{2013}\)