But if 1/y approaches infinity "faster" than the value in parentheses approaches 1, then the number raised to the power could be other than 1.

For example, as y approaches zero, (1+y)^(1/y) approaches, not 1, but rather e, the basis of "continuous compounding" for example.

In the current example of the first part of this problem, when y = 1/713623846352979940529142984724747568191373312, the portion inside parentheses is about 1.00000000000000000000000000000000000000000000194261215933945611783779011590634 and being raised to the 1/y power brings about          4.000000000000000000000000000000000000000000000897677427445074158301347400319084843059343712861