Question

1/1*3+1/3*5+1/5*7+......+1/2011*2013

如题

Answer 1

1/1*3+1/3*5+1/5*7+......+1/2011*2013
=(1-1/3+1/3-1/5+1/5-1/7+.........+1/2011-1/2013)÷2
=(1-1/2013)÷2
=1006/2013

Answer 2

1/1*3=1/2(1-1/3)
1/3*5=1/2(1/3-1/5)
1/2011*2013=1/2(1/2011-1/2013)
1/1*3+1/3*5+1/5*7+......+1/2011*2013=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/2011-1/2013)
=1/2(1-1/2013)
=1006/2013