I think the OP is using "last book" to mean the one at the bottom of the stack. (I would call the top one the last book, since it was the last one placed on the stack, but the question makes more sense if it means the bottom book.)
In that case, the answer to the question depends on what idealisation you make. If you idealise the books as non-compressible and much wider than the stack is tall so there's no significant difference in torque between the two cases, then yes you can get the same motion by applying ##n## forces of magnitude ##F## or one of magnitude ##nF##.
In reality, books are typically slightly compressible and a stack of books will frequently be taller than it is wide. In that case where you apply the force matters because it will change how the weight is distributed which may affect how easily it slides. It's a fairly common experience that pushing something at a point below its center of mass is easier than pushing it at the top.
