Question

A=(1/2+1).(1/3+1).(1/4+1)...(1/2011+1)

Answer 1

A= (1/2 + 2/2) . (1/3+3/3) . (1/4 + 4/4).....(1/2011 + 2011/2011)

A= 3/2 . 4/3 . 5/4 ..... 2012/2011

A= 2012/2 = 1006

Answer 2

\(A=\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)......\left(\frac{1}{2011}+1\right)\)

\(A=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{2012}{2011}\)

\(A=\frac{3.4.5..........2012}{2.3.4..........2011}\)

\(A=\frac{2012}{2}=1006\)

Answer 3

A=(1/2+1).(1/3+1).(1/4+1)...(1/2011+1)

=3/2.4/3.5/4...2012/2011

=2012/2=1006