Question

Please help

Answer 1

Evaluate
\[\frac{ 1}{ 1\times2 }+\frac{ 1 }{ 2\times3}+\frac{ 1 }{ 3\times4 }+...+\frac{ 1 }{ 2012\times2013 }\]

Answer 2

Ok this is real easy

Answer 3

\[\frac{ 1 }{ 1*2 }=\frac{ 1 }{ 2 }=(1-\frac{ 1 }{ 2 })\]

Answer 4

Similarly 1/(2*3)=(1/2-1/3) and others

Answer 5

So we get
1/(1*2)+1/(2*3)+1/(3*4)+...+1/(2012*2013)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2012-1/2013)=1-1/2013= 2012/2013

Answer 6

Thanks so much