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General Math Question?
If I am trying to prove one sum, from k=1 to k=say100, is equal to another sum from k=1 to k=100
so each sum has a different function, say sum(g(k)) from k=1,100 and sum(f(k)) from k=1,100.
Can I expect that for them to be equal, g(k) = f(k) always?
2 Answers
- wiseguyLv 69 years agoFavorite Answer
Dear Boa,
In general, you can't expect that if two functions have identical sums over a given interval, then the functions will be equal in that interval. That is, it is not necessarily true that
if ∑ f(k) = ∑ g(k), then f(k) = g(k), where k is in {1, . . . , n}.
To see a simple counterexample, consider the following two functions:
f(k) = k, and
g(k) = 101 - k.
You can verify that
∑ f(k) = ∑ g(k), for k in {1, 2, 3, . . . , 100}.
However, it's readily seen that for any integer k, we have f(k) ≠ g(k).
