Câu hỏi của vũ vinh

Question

so sánh A và B biết A=1515+1\1516+1 và B+=1516+1\1517+1

Lê Tài Bảo Châu · Accepted Answer

áp dụng tc $\frac{a}{b}< 1\Rightarrow\frac{a+m}{a+m}< 1\left(m\in N\right)$Ta có: $B=\frac{15^{16}+1}{15^{17}+1}< \frac{15^{16}+1+14}{15^{17}+1+14}$$=\frac{15^{16}+15}{15^{17}+15}=\frac{15.\left(15^{15}+1\right)}{15.\left(15^{16}+1\right)}=\frac{15^{15}+1}{15^{16}+1}$$\Rightarrow B< A$Câu trả lời: áp dụng tc $\frac{a}{b}< 1\Rightarrow\frac{a+m}{a+m}< 1\left(m\in N\right)$Ta có: $B=\frac{15^{16}+1}{15^{17}+1}< \frac{15^{16}+1+14}{15^{17}+1+14}$$=\frac{15^{16}+15}{15^{17}+15}=\frac{15.\left(15^{15}+1\right)}{15.\left(15^{16}+1\right)}=\frac{15^{15}+1}{15^{16}+1}$$\Rightarrow B< A$

Kiệt Nguyễn · Answer

$A=\frac{15^{15}+1}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+15}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+1+14}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+1}{15^{16}+1}+\frac{14}{15^{16}+1}$$\Rightarrow15A=1+\frac{14}{15^{16}+1}$$B=\frac{15^{16}+1}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+15}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+1+14}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+1}{15^{17}+1}+\frac{14}{15^{17}+1}$$\Rightarrow15B=1+\frac{14}{15^{17}+1}$Vì $\frac{14}{15^{17}+1}< \frac{14}{15^{16}+1}$ nên $15B< 15A$Vậy B < ACâu trả lời: $A=\frac{15^{15}+1}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+15}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+1+14}{15^{16}+1}$$\Rightarrow15A=\frac{15^{16}+1}{15^{16}+1}+\frac{14}{15^{16}+1}$$\Rightarrow15A=1+\frac{14}{15^{16}+1}$$B=\frac{15^{16}+1}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+15}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+1+14}{15^{17}+1}$$\Rightarrow15B=\frac{15^{17}+1}{15^{17}+1}+\frac{14}{15^{17}+1}$$\Rightarrow15B=1+\frac{14}{15^{17}+1}$Vì $\frac{14}{15^{17}+1}< \frac{14}{15^{16}+1}$ nên $15B< 15A$Vậy B < A

Chúng tôi đề xuất

Tài nguyên

Ứng dụng mobile

Bảng xếp hạng

Các khóa học có thể bạn quan tâm

Yêu cầu VIP