There are N processes and they share M resources.
Sum of the requirement of all processes will be " Sum of all S_{i}" ie ∑i=1nSi∑i=1nSi . Now If you dont want the deadlock to occur,then you should share M resources such that each process will get 1 less than their maximum requirement and then add 1 resource to any one of the processes. This way you can avoid deadlock.
So the expression should be like this : ∑i=1nSi∑i=1nSi- N+ 1= M meaning we are summing all requirements, then subtracting N,that is 1 resource from each of the processes' requirement, so that all Processes will be waiting. then adding 1, that is allocating 1 resource to any 1 of the processes so that it can complete its execution and leave its resources so that other process can use. This should be equal to M.
Now if you move N to RHS then expression will be like ∑i=1nSi∑i=1nSi-1 = M+N.
If clearly, now if we ignore 1, then the expression wil be reduced to ∑i=1nSi∑i=1nSi < M+N. Right.