Question

1/1*2*3+1/2*3*4+......+1/48*49*50

Answer 1

1/1*2*3+1/2*3*4+......+1/48*49*50
=(1/1*2-1/2*3+1/2*3-1/3*4+......+1/48*49-1/49*50)÷2
=(1/野派1*2-1/49*50)÷2
=(1/2-1/颂档贺2450)÷2
=612/1225÷2
=306/蠢岩1225

Answer 2

=1/2(2*2/1*2*2*3+2*3/察羡指2*3*3*4+…派悉…+2*49/48*49*49*50)
=1/败配2(1/1*2_1/2*3+1/2*3-1/3*4+……+1/48*49-1/49*50)
=1/2(1/2-1/2450)
=612/2450
=306/1225