Câu hỏi của Vũ Hoàng Thiên

Question

1 phần 12 + 1 phần 20 cộng 1 phần 30 + chấm chấm chấm + 1 phần110

Lương Thị Vân Anh · Accepted Answer

$\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{110}$

= $\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{10\times11}$

= $\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{11}$

= $\dfrac{1}{3}-\dfrac{1}{11}=\dfrac{8}{33}$Câu trả lời: $\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{110}$

= $\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{10\times11}$

= $\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{11}$

= $\dfrac{1}{3}-\dfrac{1}{11}=\dfrac{8}{33}$