Look again.
The sum of the first p terms is:
Hello I was having trouble with this problem and was wondering if anybody could help me with it. Show that if the sum of the first p terms of an arithmetic progression is equal to the sum of the first q terms, where p q, then the sum of the first p + q terms must be zero.
I do not really know where to start; I came up with this but it is not helpful:
which of course shows that p = q even though it does not.
Thanks and happy new year!
We will follow what you did,
Not really, it says p=q could be possible, but it doesn't say p=q is the only thing possible.
What is the sum of first p+q terms??
We want to show S=0 ,i.e --------------(*)
Let us see why,
Since we are forced to conclude
which is nothing but (*).
All done