Câu hỏi của Nguyễn Thị Hạnh

Question

A = 2/1.4 + 2/4.7 + 2/7.10 + 2/97 . 100

Nguyễn Thanh Hằng · Accepted Answer

$A=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+...................+\dfrac{2}{97.100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{3}{2}\left(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+..................+\dfrac{2}{97.100}\right)$

$\Rightarrow\dfrac{3}{2}A=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...................+\dfrac{3}{97.100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+..............+\dfrac{1}{97}-\dfrac{1}{100}$

$\Rightarrow\dfrac{3}{2}A=1-\dfrac{1}{100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{99}{100}$

$\Rightarrow A=\dfrac{99}{100}:\dfrac{3}{2}$

$\Rightarrow A=\dfrac{33}{50}$Câu trả lời: $A=\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+...................+\dfrac{2}{97.100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{3}{2}\left(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+..................+\dfrac{2}{97.100}\right)$

$\Rightarrow\dfrac{3}{2}A=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...................+\dfrac{3}{97.100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+..............+\dfrac{1}{97}-\dfrac{1}{100}$

$\Rightarrow\dfrac{3}{2}A=1-\dfrac{1}{100}$

$\Rightarrow\dfrac{3}{2}A=\dfrac{99}{100}$

$\Rightarrow A=\dfrac{99}{100}:\dfrac{3}{2}$

$\Rightarrow A=\dfrac{33}{50}$