The relationship between the power of N + 1 and the power of N + 1

The relationship between the power of N + 1 and the power of N + 1

The former is larger when n ≤ 2, and the latter is larger when n ≥ 3
Proof: obviously both are positive numbers
(n+1)^n/n^(n+1)=(1+1/n)^n/n
∵n∈N*,∴(1+1/n)^n

The size relationship between the n-th power of N plus 1 and the n-th power of N plus 1
Come on!

Expand (n + 1) ^ n to n ^ n + 1 + I can't remember clearly, but there must be the first two terms. Then I use the ratio method, that is, n ^ n / (n + 1) ^ n = n ^ n / (n ^ n + 1 +...)

The power of (n-1) is larger than that of (n-1)
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Because n > 1, when 11
That is, f (x) > G (x) holds