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I am guessing that this is correct for 3-EXP, 4-EXP etc...

Basically I should find a problem in 2-EXP that is not in EXP. Any examples ?

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It is a direct consequence of the time hierarchy theorem:

Time Hierarchy Theorem: if f and g are time-constructible functions and $f(n) \log f(n) = o(g(n))$ (e.g. $f(n) = n^2, g(n) = n^3$), then $DTIME(f(n)) \subsetneq DTIME(g(n))$

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