The main theoretical basis of scaling method (1) the transitivity of inequality;
(2) Equal amount plus unequal amount is unequal amount;
(3) Comparison of two fractions with the same numerator but different denominator.
Scaling method is a thinking method that guides the direction of deformation through inequality proof.
The common techniques of scaling (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.
Example 1] Proof:1/2-1(n+1) <1/2 2+/3 2+...+/kloc. (n- 1)/n (n=2,3,4...)
Solution: ∫1/22+1/32+...1/N2 >1/2 * 3+1/3 * 4+...
1/2^2+ 1/3^2+...... 1/n^2<; 1/ 1 * 2+ 1/2 * 3+ 1/(n- 1)* n = 1- 1/2+65438。
∴ 1/2- 1/(n- 1)<; 1/2^2+ 1/3^2+......+ 1/n^2<; (n- 1)/n