2a=1+1/2+1/2^2+..............+1/2^2014+1/2^2015

2a-a=(1+1/2+1/2^2+.............+1/2^2014+1/2^2015)-(1/2+1/2^2+1/2^3+..........+1/2^2015+1/2^2016)

a=1-1/2^2016

a=2^2016-1/2^2016

vậy a =2^2016/2^2016

bằng 15 hay sao ý

Ta có :

\(S=2015+\frac{2015}{1+2}+\frac{2015}{1+2+3}+...+\frac{2015}{1+2+3+..+2016}\)

    \(=2015.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+..+2016}\right)\)

    \(=2015.\left(1+\frac{1}{\frac{\left(2+1\right).2}{2}}+\frac{1}{\frac{\left(3+1\right).3}{2}}+...+\frac{1}{\frac{\left(2016+1\right).2016}{2}}\right)\)

    \(=2015.\left(\frac{2}{2}+\frac{2}{2.\left(2+1\right)}+\frac{2}{3.\left(3+1\right)}+...+\frac{2}{2016.\left(2016+1\right)}\right)\)

    \(=2015.2.\left(\frac{1}{2}+\frac{1}{2.\left(2+1\right)}+\frac{1}{3.\left(3+1\right)}+...+\frac{1}{2016.\left(2016+1\right)}\right)\)

    \(=2015.2.\left(\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2016.2017}\right)\)

    \(=2015.2.\left(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2016}-\frac{1}{2017}\right)\) 

    \(=2015.2.\left(\frac{1}{2}+\frac{1}{2}-\frac{1}{2017}\right)\)

    \(=2015.2.\left(1-\frac{1}{2017}\right)\)

    \(=2015.2.\frac{2016}{2017}\)

    =\(\frac{2015.2.2016}{2017}\)

    =\(\frac{8124480}{2017}\)

Vậy \(S=\frac{8124480}{2017}\)

Sai vì ngoài học tập ra còn cần phải siêng năng chăm chỉ trong các lĩnh vực khác nửa như giúp đỡ mọi người ,tham gia các hoạt động rèn luyện

           \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(\Leftrightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2014}}+\frac{1}{2^{2015}}\)

\(\Leftrightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)\)

\(\Leftrightarrow\)\(A=1-\frac{1}{2^{2016}}\)

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

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

\(2A-A=\left(1+\frac{1}{2}+.....+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{2016}}\right)\)

\(A=1-\frac{1}{2^{2016}}\)

2A= 1+ 1/2 + 1/2^2+....+1/2^2015

2A -A= (1+1/2+1/2^2+...+1/2^2015)-(1/2+1/2^2+...+1/2^2016)

A= 1-\(\frac{1}{2^{2016}}\)

Đáp số: A=1-\(\frac{1}{2^{2016}}\)

=2015/2016

Đặt \(A=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+.......+\frac{2}{2015}+\frac{1}{2016}\)

\(=\frac{2015}{2}+1+\frac{2014}{3}+1+...........+\frac{1}{2015}+1\)

\(=\frac{2017}{2}+\frac{2017}{3}+.........+\frac{2017}{2015}+\frac{2017}{2016}\)

\(=2017.\left(\frac{1}{2}+\frac{1}{3}+.......+\frac{1}{2015}+\frac{1}{2016}\right)\)

Thay A vào biểu thức ta dc

\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{2017}}{A}\)

\(=\frac{\frac{1}{2017}}{2017}\)\(=1\)

CÓ THỂ LÀ SAI NÊN BẠ THÔNG CẢM CHO MK

sai rôi bạn ơi