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Junior high school mathematics. quadratic radical
Take the reciprocal

1/ (root number n+2- root number n+ 1) Both the numerator and denominator are multiplied by root number n+2+ root number n+ 1.

= (radical number n+2+ radical number n+ 1) (1)

Similarly, both the numerator and denominator of1(root number n+ 1- root number n) are multiplied by the root number n+ 1+ root number n.

= (root number n+ 1+ root number n) (2)

(1)>(2) According to the reciprocal nature, we can know that

Root number n+2- root number n+ 1