Higher level maths

(1-x-1/x)⁷

= [1-(x+1/x)]⁷

= (1)⁷(x+1/x)⁰ - 7(1)⁶(x+1/x)¹ + 21(1)⁵(x+1/x)² - 35(1)⁴(x+1/x)³+ 35(1)³(x+1/x)⁴ - 21(1)²(x+1/x)⁵ + 7(1)¹(x+1/x)⁶ - (1)⁰(x+1/x)⁷

constant term in (1)⁷(x+1/x)⁰ = 1

constant term in - 7(1)⁶(x+1/x)¹ = 0

constant term in 21(1)⁵(x+1/x)² = (21)(2) = 42

constant term in - 35(1)⁴(x+1/x)³ = 0

constant term in + 35(1)³(x+1/x)⁴ = (35)(6) = 210

constant term in - 21(1)²(x+1/x)⁵ = 0

constant term in 7(1)¹(x+1/x)⁶ = (7)(20) = 140

constant term in - (1)⁰(x+1/x)⁷ = 0

constant term in [1-(x+1/x)]⁷ = 1 + 42 + 210 + 140 = 393


2013-12-20 15:50:25 補充：
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 32 32 21 7 1