i have checked the problem number and everything...i think there is a massive misprint as i have done some other questions from the same section and the answers all seem to be wrong as there are of the same format as the answer in the first post!
I have worked out the limit as x tends towards +infinity for cos(1/x) to be 1, as cos (1/infinity) would be cos(0) which is 1. However the answer in the book with the question says that the answer should be (0,3) and (3,+infinty)! Is this a misprint or have i gine drastically wrong?
im stuck on this proof can anyone help?
Is it true that for all natural numbers n, for each natural number x, x^n − x is
divisible by n? If so, prove it; if not, explain why not.
so far i have gotten:
make x=1, ((1)^n) -1 = 0, therefore x=1 is divisible by n
assume true for x=k...