On a railway there are 20 stations. The no of different tickets required in order that it may be possible to travel from every station to every station.

we have to add 20 +19+18+...+3+2+1 to get the answer ..Is there any SHORTCUT TO SOLVE IT IN LESS TIME ??

Hello student,
please find the answer to your question below
Given that on a railway there are 20 stations and asked to find out the no of different tickets required in order that it may be possible to travel from every station to every station.
The solution can be obtained by simply adding the ways=20+19+.....+1
for which we have a formula=n(n+1)/2=21(20)/2=210.
This is the simplest way.