Take a closer look at each of the following formulas and calculate to see what you can find? （1）1／2×1／3＝1/6 1/2-1/3＝1/6 (2)1/3×1/4=1/12 1/3-1/4=1/12 . (5) What rules do you find through calculation? （6）1/2+1/6+1/12+1/20+1/30+1/42=? I am in a hurry!

Take a closer look at each of the following formulas and calculate to see what you can find? （1）1／2×1／3＝1/6 1/2-1/3＝1/6 (2)1/3×1/4=1/12 1/3-1/4=1/12 . (5) What rules do you find through calculation? （6）1/2+1/6+1/12+1/20+1/30+1/42=? I am in a hurry!

_ What rule do you find through calculation? 1 / N × 1 / (n + 1) = 1 / n-1 / (n + 1) (6) 1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 = 1 / (1 * 2) + 1 / (2 * 3) + 1 / (3 * 4) + 1 / (4 * 5) + 1 / (5 * 6) + 1 / (6 * 7) = 1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + 1 / 5-1 / 6-1 / 7 = 1-1 / 7 = 6 / 7

Operation law and simple calculation (additive commutation law, associative law; multiplicative commutation law, associative law and distributive law)

Additive commutative law: a + B = B + A
The law of combination of addition: a + B + C = a + (B + C)
Commutative law of multiplication: a × B = B × a
The combination law of multiplication: a × B × C = a × (B × C)
Multiplicative distribution law: a × (B + C) = a × B + a × C

Observe the following figures and their corresponding formulas, and calculate 1 + 8 + 16 + 24 + according to the rule you found +The result of 8N (n is a positive integer) is ()
A. （2n+1）2B. （2n-1）2C. （n+2）2D. n2

Graph (1): 1 + 8 = 9 = (2 × 1 + 1) 2; graph (2): 1 + 8 + 16 = 25 = (2 × 2 + 1) 2; graph (3): 1 + 8 + 16 + 24 = 49 = (3 × 2 + 1) 2 Then graph (n): 1 + 8 + 16 + 24 + +8N = (2n + 1) 2

Observe the figure in the figure and its corresponding formula, and calculate 1 + 8 + 16 + 24 + ··· + 8N (n is a positive integer) according to the rule you found

8（1+2+3+4+.+n）=8（n+1\2）=4（n+1）=4n+4