For a generic symbol A[i]
2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}]
does not return True.
Is there any reason behind these behaviors? Do we have any way to evaluate the equation correctly?
ADDED:
I would like to thank everyone who noted the comments. I am afraid my use of Simplify makes everyone confused. I want to ask not the behavior of Simplify, but that of Sum and Equal. Is it intentional or kind of a "bug"?
Edited:
What I would like to ask is about Sum and I have not intended to ask the use of Simplify. So, I edited the title again.
As I have written below, mathematically Sum[2 ..] is equivalent to 2 Sum[..]. I thought that as long as mathematically correct, Mathematica returns immediate values, especially for trivial cases, just like the examples of a + b == b + a or a b == b a. Does not this hold for Sum? Do we have any way to let Mathematica evaluate the relation mathematically correctly? This is my question. I am sorry if my question was ambiguous.
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