em ko biết,vì em học lớp 5

Khi a=1/2015 thì \(P=\left|\dfrac{1}{2015}-\dfrac{1}{2014}\right|+\left|\dfrac{1}{2015}-\dfrac{1}{2016}\right|\)

\(=\dfrac{1}{2014}-\dfrac{1}{2015}+\dfrac{1}{2015}-\dfrac{1}{2016}\)

\(=\dfrac{1}{2014}-\dfrac{1}{2016}=\dfrac{2}{2014\cdot2016}=\dfrac{1}{1008\cdot2014}\)

\(=\dfrac{1}{2030112}\)

\(\left(-3\right)^{2015}x\left(\frac{1}{3}\right)^{2015}+\left(0.25\right)^{2016}x4^{2016}\)

=\(\left(-3x\frac{1}{3}\right)^{2015}+\left(0.25x4\right)^{2016}\)

=\(\left(-1\right)^{2015}+1^{2016}\)

=\(-1+1\)

=\(0\)

Thay \(a=2015\)vào biểu thức \(P=|a-\frac{1}{4}|+|a-\frac{1}{2016}|\), ta có :

\(P=|2015-\frac{1}{4}|+|2015-\frac{1}{2016}|\)

\(P=|\frac{8060}{4}-\frac{1}{4}|+|\frac{4062240}{2016}-\frac{1}{2016}|\)

\(P=|\frac{8059}{4}|+|\frac{4062239}{2016}|\)

\(P=\frac{8059}{4}+\frac{4062239}{2016}\)

\(P=\frac{4061736}{2016}+\frac{4062239}{2016}\)

\(P=\frac{8123975}{2016}\)

Vậy giá trị biểu thức P tại \(a=2015\)là \(\frac{8123975}{2016}\)

học tốt

\(A=1+2+...+2^{2015}+2^{2016}\)

\(2A=2+2^2+...+2^{2016}+2^{2017}\)

\(2A-A=\left(2+2^2+...+2^{2017}\right)-\left(1+2+...+2^{2016}\right)\)

\(A=2^{2017}-1\)

\(B=2^{2016}+2^{2015}+2^{2014}+...+2+1\)

\(\Rightarrow B=1+2+...+2^{2014}+2^{2015}+2^{2016}\)

\(\Rightarrow2B=2+2^2+...+2^{2015}+2^{2016}+2^{2017}\)

\(\Rightarrow2B-B=2^{2017}-1\Rightarrow B=2^{2017}-1\)

Đặt C=1+2+....+2²⁰¹⁵+2²⁰¹⁶

=> 2C=2+2²+2³+....+2²⁰¹⁷

=>  2C-C=2²⁰¹⁷--1

=>C = 2²⁰¹⁷--1