Question

1÷1×2+1÷2×3+1÷3×4+……+1÷2015×2016=2015/2016

Answer 1

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(2015*2016)

=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/2015-1/2016)

=1/1-1/2016

=2015/2016

Answer 2

1÷(1×2)+1÷(2×3)+1÷(3×4)+……+1÷(2015×2016)
=(1-2分之1)+(2分之1-3分之1)+(3分之1-4分之1)+......+(2015分之1-2016分之1)
=1-2分之1+2分之1-3分之1+3分之1-4分之1+......2015分之1-2016分之1
=1-2016分之1
=2016分2015