The common strategies to prove inequality by "scaling method" are: scaling first and then summing (or summing first and then scaling); Add or discard some positive items (or negative items); Zoom first, then crack the item (or crack the item first and then zoom); Enlarge or reduce the "factor"; Enlarge or reduce item by item; Fix some items and scale others; Scaling by using basic inequalities; First combine and sort properly, and then compare or scale one by one.

Scaling means making inequality

Extended data:

Expand skills:

(1) Omit (or add) some items.

(2) Enlarge or reduce the numerator or denominator in the fraction.

(3) Scaling by applying basic inequalities (such as mean inequality).

(4) Monotonicity of the function is applied to scaling.

(5) Scale according to the topic conditions.

(6) Construct geometric series to scale.

(7) Scaling is carried out under the condition of structural cracks.

(8) Use the tangent and secant approximation of the function to scale.

(9) Scaling by using the split item method.

(10) Zoom in and out by dislocation subtraction.

Baidu Encyclopedia-Zooming Method