Question

\(1/2016.2015+1/2015.2014+...+1/1.2\)

Answer 1

\(\frac{1}{2016.2015}+\frac{1}{2015.2014}+...+\frac{1}{1.2}\)

\(=\frac{1}{1.2}+...+\frac{1}{2014.2015}+\frac{1}{2015.2016}\)

\(=\frac{1}{1}-\frac{1}{2}+...+\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2016}\)

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

\(=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)

~ Hok tốt ~

Answer 2

=1/2016-1/2015+1/2015-1/2014+...+1-1/2

=1/2016-1/2

=-1007/2016

Answer 3

\(\frac{1}{2016.2015}+\frac{1}{2015.2014}+...+\frac{1}{1.2}\)

\(=\frac{1}{2016}-\frac{1}{2015}+\frac{1}{2015}-\frac{1}{2014}+...+\frac{1}{2}-\frac{1}{1}\)

\(=\frac{1}{2016}-1\)

\(=-\frac{2015}{2016}\)