Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
A= \(\frac{2016^{16}+1}{2016^{17+1}}\) B=\(\frac{^{2016^{17}+1}}{2016^{18}+1}\)
2016A=\(\frac{2016^{17}+17}{2016^{17}+1}\) 2016B=\(\frac{2016^{18}+17}{2016^{18}+1}\) (gap 2016 lan)
2016A=\(1+\frac{16}{2016^{17}+1}\) 2016B=\(1+\frac{16}{2016^{18}+1}\)
ta co 1+\(\frac{16}{2016^{17}+1}\) > 1+\(\frac{16}{2016^{18}+1}\)
suy ra 2016A>2016B
K/L: A>B
nhi k do
a ) so sánh 2016^2017 + 2016^2016 với 2017^2017
A = 2016^2017 + 2016^2016
A = 2016^2016.(2016 + 1)
A = 2016^2016.2017 < 2017^2016.2017 = 2017^2017
Vậy 2016^2017 + 2016^2016 < 2017^2017
b) Biết x - 5y chia hết cho 17 . CMR : 10x + y chia hết cho 17
(x - 5y) ⋮ 17
10(x - 5y) ⋮ 17
(10x - 50y) ⋮ 17
(10x - 50y + 51y) ⋮ 17
(10x + (51y - 50y)) ⋮ 17
(10x + y) ⋮ 17 (đpcm)
- \(A=\frac{2015}{2016}+\frac{2016}{2017}>1;\)
- \(B=\frac{2015+2016}{2016+2017}< 1\)
- Nên A>B
\(A=\frac{2015}{2016}+\frac{2016}{2017}=1-\frac{1}{2016}+1-\frac{1}{2017}>1\)
\(B=\frac{2015+2016}{2016+2017}< \frac{2016+2017}{2016+2017}=1\)
Suy ra \(A>B\).
a, Ta có :
\(A=\dfrac{15}{14}+\dfrac{16}{15}+\dfrac{17}{16}+\dfrac{18}{17}\)
\(\Leftrightarrow A=\left(1+\dfrac{1}{14}\right)+\left(1+\dfrac{1}{15}\right)+\left(1+\dfrac{1}{16}\right)+\left(1+\dfrac{1}{17}\right)\)
\(\Leftrightarrow A=\left(1+1+1+1\right)+\left(\dfrac{1}{14}+\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}\right)\)
\(\Leftrightarrow A=4+\left(\dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}+\dfrac{1}{18}\right)\)
\(\Leftrightarrow A>4\)
b. \(B=\dfrac{2015}{2016}+\dfrac{2016}{2017}+\dfrac{2017}{2019}\)
\(\Leftrightarrow B=\left(1-\dfrac{1}{2016}\right)+\left(1-\dfrac{1}{2017}\right)+\left(1-\dfrac{3}{2019}\right)\)
\(\Leftrightarrow B=\left(1+1+1\right)-\left(\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{3}{2019}\right)\)
\(\Leftrightarrow B=3-\left(\dfrac{1}{2016}+\dfrac{1}{2017}+\dfrac{3}{2019}\right)\)
\(\Leftrightarrow B< 3\)