When x tends to infinity, how can the limit of (1 + 1 / x) ^ x not be 1, but e?

Let t = 1 / x, then s = (1 + 1 / x) ^ x = (1 + T) ^ (1 / T), X tends to ∞, then t tends to 0
LNs = ln (1 + T) / T, when t tends to 0, the numerator denominator tends to 0, so we can use the law of Robida to derive the numerator denominator
Then LNs tends to 1 / (1 + T) = 1, obviously s tends to E

When x tends to infinity, how can the limit of (1 + 1 / x) ^ x not be 1, but e?

When x tends to infinity, how can the limit of (1 + 1 / x) ^ x not be 1, but e?

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