Your two-step analysis can't come to a valid conclusion, including proving it wrong. In fact, solving the problems of advanced mathematics requires the tools of advanced mathematics.

Prove:

A tool of advanced mathematics-McLaughlin formula with Lagrange remainder

Take it:

There are:

Therefore:

Extended data:

This problem actually applies Bernoulli inequality:

It is easy to see that the equal sign holds if and only if n=0, 1 or x=0.

Bernoulli inequality is often used as a key step to prove other inequalities.

The general formula of Bernoulli inequality is:

In addition, McLaughlin formula has great application space in order estimation, and the common expansions are as follows:

References:

Baidu Encyclopedia-McLaughlin Formula?

Baidu Encyclopedia-Taylor Formula

3.？ Baidu encyclopedia-Bernoulli inequality

4. Baidu Library-Typical Integral