Tính giá trị biểu thức
A=\(2^{2015}-\left(2^{2014}+2^{2013}+...+2+1\right)\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(C=\dfrac{2014\left(2015^2+2016\right)-2016\left(2015^2-2014\right)}{2014\left(2013^2-2012\right)-2012\left(2013^2+2014\right)}\)
\(=\dfrac{2.2014.2016+2014.2015^2-2016.2015^2}{2014.2013^2-2012.2013^2-2.2012.2014}\)
\(=\dfrac{2.\left(2015+1\right)\left(2015-1\right)-2.2015^2}{2.2013^2-2.\left(2013+1\right)\left(2013-1\right)}\)
\(=\dfrac{2.\left(2015^2-1\right)-2.2015^2}{2.2013^2-2.\left(2013^2-1\right)}=\dfrac{-2}{2}=-1\)
\(E=\left(2016-2015\right)\left(2016+2015\right)+\left(2014-2013\right)\left(2014+2013\right)+...+\left(2-1\right)\left(2+1\right)\\ E=2016+2015+2014+2013+...+2+1\\ E=\left(2016+1\right)\left(2016+1-1\right):2\\ E=2033136\)
\(A=2^{2015}-\left(2^{2014}+2^{2013}+...+2+1\right)\)
Đặt \(B=2^{2014}+2^{2013}+...+2+1\)
\(\Rightarrow2B=2^{2015}+2^{2014}+...+2^2+2\)
\(\Rightarrow2B-B=\left(2^{2015}+2^{2014}+...+2^2+2\right)-\left(2^{2014}+2^{2013}+...+2+1\right)\)\(\Rightarrow B=2^{2015}-1\)
\(\Rightarrow A=2^{2015}-2^{2015}+1\)
\(\Rightarrow A=1\)
cảm ơn bạn nhìu![vui vui](https://hoc24.vn/media/cke24/plugins/smiley/images/vui.png)