After travelling how much distance mathematician will fall into the pit?

Question

Consider a mathematician standing at a point 'P'. He travels 1 meter initially in forward direction and from there, 0 meter in backward direction. Then from that position he travels 2 meters in forward direction and 1 meter in backward direction. Again from the position resulting from previous steps he goes 3 meters in forward and then 2 meters in backward direction(Note carefully the pattern he follows). There is a pit 2018 meter from the starting point. After traveling how much distance(in meters) he will fall into the pit?

Answer 1

1019090 m

The distance from point P to pit is 2018 m

step one- 1 m forward, 0 m backward, travel 1 m, distance from P 1m,
every next step- +1 m forward, +1 m backward, travel +2 m, distance from P +1 m
...
...
step 1008, 1008 m forward, 1007 m backward, travel 2015 m, distance from P 1008 m
step 1009, 1009 m forward, 1008 m backward, travel, 2017 m, distance from P 1009 m
at step 1010, 1009 m forward and fall into pit, 0 m backward, travel 1009, distance from P 2018 m and into pit

total travel will be (1+2017)*1009/2 (for 1009 steps) +1009 (for last step)=1019090 m