Câu hỏi của Bùi Xuân Doanh

Question

$\dfrac{1}{24}+\dfrac{1}{60}+\dfrac{1}{240}+...+\dfrac{1}{990}$

Đoàn Trần Quỳnh Hương · Accepted Answer

$2.B=\dfrac{2}{6}+\dfrac{2}{14}+\dfrac{2}{60}+...+\dfrac{2}{990}$

$2B=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{9.10.11}$

$2B=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{9.10}-\dfrac{1}{10.11}$

$2B=\dfrac{1}{1.2}-\dfrac{1}{10.11}$

$B=\dfrac{27}{110}$Câu trả lời: $2.B=\dfrac{2}{6}+\dfrac{2}{14}+\dfrac{2}{60}+...+\dfrac{2}{990}$

$2B=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+...+\dfrac{2}{9.10.11}$

$2B=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{9.10}-\dfrac{1}{10.11}$

$2B=\dfrac{1}{1.2}-\dfrac{1}{10.11}$

$B=\dfrac{27}{110}$