Prove the statement //////////

If ∑(k=a,b) f(k) = ∑(k=a,b) g(k) for all a and b
then, putting a=b=n
∑(k=n,n) f(k) = ∑(k=n,n) g(k)
f(n) = g(n).
As n could be any positive integer, we have f(n) ≡ g(n).

2012-07-05 13:16:01 補充：
PS: I misunderstand that f and g are definded on integers because ∑(k=a,b) is involved. I agree with 自由自在's explanation that the statement is false when the domains of f and g contain more than integers.

Suppose f(x)=x and g(x)=[x]
For all integer operations, the results are equal
but the 2 functions are not identical