So, this assumes that all packets are the same length and all links are the same bandwidth.
I think a mistake you are making is that your formula looks at the end-to-end delay for a single packet, then multiplies it by the number of packets. In this case, the first packet would be sent end-to-end, then the second packet would be send end-to-end etc.
In a real network, once the first link has finished transporting the first packet, the first packet moves onto the second link. At this stage, the first link can begin transporting the second packet. Once the first and second links have finished transporting the second and first packets (respectively), they can now move onto the second and third links, while the first link starts transporting the third packet etc.
So really, you need to look at the time taken to send all packets across the first link, one-by-one, then look at the time taken for the last packet to traverse the remaining links.
So if you consider (L/R) as the time taken to transport one packet across one link.
Then consider there are P of these delays to transport all packets over the first link, one-by-one
And there are (N-1) of these delays to transport the last packet over the remaining links
Then the formula for this would be:
(P + (N-1)) * (L/R)
Note: this formula is very simplistic and assumes there are no propagation delays, node processing delays or queuing delays etc.