Câu hỏi của Fgeaioawd

Question

So sánh A=1/3 + 1/6 + 1/10 +...+1/561 với phân số 8/9

Lê Thị Linh Chi · Accepted Answer

$A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{561}$$A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{1122}$$A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{33.34}$$A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{33.34}\right)$$A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{33}-\frac{1}{34}\right)$$A=2.\left(\frac{1}{2}-\frac{1}{34}\right)$$A=2.\left(\frac{17-1}{34}\right)$$A=2.\frac{8}{17}$$A=\frac{16}{17}>\frac{16}{18}=\frac{8}{9}$$\Rightarrow A>\frac{8}{9}$Câu trả lời: $A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{561}$$A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{1122}$$A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{33.34}$$A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{33.34}\right)$$A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{33}-\frac{1}{34}\right)$$A=2.\left(\frac{1}{2}-\frac{1}{34}\right)$$A=2.\left(\frac{17-1}{34}\right)$$A=2.\frac{8}{17}$$A=\frac{16}{17}>\frac{16}{18}=\frac{8}{9}$$\Rightarrow A>\frac{8}{9}$

Chúng tôi đề xuất

Tài nguyên

Ứng dụng mobile

Bảng xếp hạng

Các khóa học có thể bạn quan tâm

Yêu cầu VIP