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This is not a homework problem. It was stated in a textbook as trivial but I cannot prove it myself in general. If [A,B]=0 then [A,B^n] = 0 where n is a positive integer. This seems rather intuitive and I can easily see it to be true when I plug in n=2, n=3, n=4, etc. However, I cannot prove it in the general case and this really bothers me. Here's what I got so far:
[A,B^n] = [A,BB^n-1] = [A,B]B^n-1 + B[A,B^n-1] = 0 + B[A,B^n-1]
Not sure where to go from here???
Thanks so much.
[A,B^n] = [A,BB^n-1] = [A,B]B^n-1 + B[A,B^n-1] = 0 + B[A,B^n-1]
Not sure where to go from here???
Thanks so much.