\(\frac{2014}{2015}\)\(\times\)\(\frac{1}{2}\)\(+\)\(\frac{2014}{2015}\)\(\times\)\(\frac{-2}{3}\)\(-\)\(\frac{5}{6}\)\(\div\)\(\frac{2014}{2015}\)
Những câu hỏi liên quan
Tính tích
\(\left(1-\frac{1}{2014}\right)\times\left( 1-\frac{2}{2014}\right)\times\left(1-\frac{3}{2014}\right).....\left(1-\frac{2015}{2014}\right)\)
tìm x biết \(\left(1+\frac{1}{2}+\frac{1}{3}+.....+\frac{1}{2015}\right)\times x+2015=\frac{2016}{1}+\frac{2017}{2}+.....+\frac{4029}{2014}+\frac{4030}{2015}\)
\(\frac{2015}{2014^2+1}+\frac{2015}{2014^2+2}+\frac{2015}{2014^2+3}+...+\frac{2015}{2014^2+2014}\)
chứng minh rằng A không phải số nguyên dương
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2015}+\frac{1}{2016}}{\frac{2015}{1}+\frac{2014}{2}+\frac{2013}{3}+...+\frac{1}{2014}+\frac{1}{2015}}\)
xét mẫu(chỗ 1/2014 sửa lại thành 2/2014)
=(1/2015+1)+(2/2014+1)+...+(2013/3+1)+(2014/2+1)+(2015/1-2014)
=2016/2015+2016/2014+...+2016/3+2016/2+1
=2016.(1/2016+1/2015+...+1/4+1/3+1/2)
=> A= 1/2016
mún dễ hỉu hơn hãy gửi tin nhắn cho mik
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Tính:
\(\frac{1}{1+\frac{2013}{2014}+\frac{2013}{2015}}+\frac{1}{1+\frac{2014}{2015}+\frac{2014}{2013}}+\frac{1}{1+\frac{2015}{2013}+\frac{2015}{2014}}\)
1) CMR : A=(n+2015)(n+2016) + n2 + n chia hết cho 2 với n ϵ N
2) So sánh :
P = \(\frac{2013}{2014^{2013}}+\frac{2014}{2015^{2014}}+\frac{2015}{2016^{2015}}+\frac{2016}{2017^{2016}}\) và
Q = \(\frac{2014}{2017^{2016}}+\frac{2013}{2016^{2015}}+\frac{2016}{2015^{2014}}+\frac{2015}{2014^{2013}}\)
A = (n + 2015)(n + 2016) + n2 + n
= (n + 2015)(n + 2015 + 1) + n(n + 1)
Tích 2 số tự nhiên liên tiếp luôn chia hết cho 2
=> (n + 2015)(n + 2015 + 1) chia hết cho 2
n(n + 1) chia hết cho 2
=> (n + 2015)(n + 2015 + 1) + n(n + 1) chia hết cho 2
=> A chia hết cho 2 với mọi n \(\in\) N (đpcm)
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a) Tính :
\(3\frac{1}{2}+\frac{2014}{2015}-0,5+\frac{1}{2015}\)
b) Tìm x :
\(85\%\times x+25\%\times x=110\)
a) Ta có: \(3\frac{1}{2}+\frac{2014}{2015}-0,5+\frac{1}{2015}\)
\(=\frac{7}{2}-\frac{1}{2}+1\)
\(=3+1=4\)
b) Ta có: \(85\%\cdot x+25\%\cdot x=110\)
\(\Leftrightarrow x\left(85\%+25\%\right)=110\)
\(\Leftrightarrow x\cdot110\%=110\)
\(\Leftrightarrow x\cdot\frac{11}{10}=110\)
hay \(x=110:\frac{11}{10}=110\cdot\frac{10}{11}=100\)
Vậy: x=100
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Tính: \(A=1+\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+............+\frac{2014}{2^{2014}}+\frac{2015}{2^{2015}}\)
\(A=1+\frac{1}{2}+\frac{2}{2^2}+...+\frac{2014}{2^{2014}}+\frac{2015}{2^{2015}}\)
\(2A=2+1+\frac{2}{2}+\frac{3}{2^2}+...+\frac{2014}{2^{2013}}+\frac{2015}{2^{2014}}\)
Trừ dưới cho trên:
\(A=2+0+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}-\frac{2015}{2^{2015}}\)
\(A=2-\frac{2015}{2^{2015}}+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)
Xét \(B=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2014}}\)
\(2B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2013}}\)
Trừ dưới cho trên: \(B=1-\frac{1}{2^{2014}}\)
\(\Rightarrow A=2-\frac{2015}{2^{2015}}+1-\frac{1}{2^{2014}}=3-\left(\frac{2015}{2^{2015}}+\frac{1}{2^{2014}}\right)\)
Nhìn thế này chắc đề yêu cầu so sánh với 3
RGBT:
E=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{2015\sqrt{2014}+2014\sqrt{2015}}+\frac{1}{2016\sqrt{2015}+2015\sqrt{2016}}\)
Ta có:
\(\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n+1}+\sqrt{n}\right)}\)
\(=\frac{\left(\sqrt{n+1}-\sqrt{n}\right)}{\sqrt{n\left(n+1\right)}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}\)
Thế vô bài toán được
\(\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}+2015\sqrt{2016}}\)
\(=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\)
\(=1-\frac{1}{\sqrt{2016}}\)
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