Question

D= 1/1x2x3+ 1/2x3x4+.....+1/2015x2016x2017

Answer 1

\(D=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{2015.2016.2017}\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2015.2016}-\frac{1}{2016.2017}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2016.2017}\right)=\frac{1}{2}.\left(\frac{2016.2017:2-1}{2016.2017}\right)\)

Answer 2

D=1/1.2.3+1/2.3.4+....+1/2015.2016.2017

D=1/2(1/1.2-1/2.3+1/2.3-1/3.4+.......+1/2015.2016-1/2016.2017)

D=1/2(1/1.2-1/2016.2017)

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