1)
Треугольник Паскаля k (1) = 1, k (2) = 5, k (3) = 10, k (4) = 10, k (5) = 5, k (6) = 1
C0/5=C5/5=1
C1/5=C4/5=5!/1!4!=5
C2/5=C3/5=5!/3!2!=1*2*3*4*5/1*2*3*1*2=120/12=10
(x-1) ^5 = x^5-5x^4+10x3-10x2+5x-1
(x+1) ^7
2) Треугольник Паскаля k (1) = 1, k (2) = 7, k (3) = 21, k (4) = 35, k (5) = 35, k (6) = 21, k (7) = 7, k (8) = 1
C0/7=C7/7=1
C1/7=C6/7=7!/1!6!=7
C2/7=C5/7=7! (5!2!) = 1*2*3*4*5*6*7/1*2*3*4*5*1*2=5040/240=21
C3/7=C4/7=7!/3!2!=1*2*3*4*5*6*7/1*2*3*4*1*2*3=5040/144=35
x^7+7x^6+21x^5+35x^4+35x^3+21x^2+7x+1
1)
Треугольник Паскаля k (1) = 1, k (2) = 5, k (3) = 10, k (4) = 10, k (5) = 5, k (6) = 1
C0/5=C5/5=1
C1/5=C4/5=5!/1!4!=5
C2/5=C3/5=5!/3!2!=1*2*3*4*5/1*2*3*1*2=120/12=10
(x-1) ^5 = x^5-5x^4+10x3-10x2+5x-1
(x+1) ^7
2) Треугольник Паскаля k (1) = 1, k (2) = 7, k (3) = 21, k (4) = 35, k (5) = 35, k (6) = 21, k (7) = 7, k (8) = 1
C0/7=C7/7=1
C1/7=C6/7=7!/1!6!=7
C2/7=C5/7=7! (5!2!) = 1*2*3*4*5*6*7/1*2*3*4*5*1*2=5040/240=21
C3/7=C4/7=7!/3!2!=1*2*3*4*5*6*7/1*2*3*4*1*2*3=5040/144=35
x^7+7x^6+21x^5+35x^4+35x^3+21x^2+7x+1
1)
Треугольник Паскаля k (1) = 1, k (2) = 5, k (3) = 10, k (4) = 10, k (5) = 5, k (6) = 1
C0/5=C5/5=1
C1/5=C4/5=5!/1!4!=5
C2/5=C3/5=5!/3!2!=1*2*3*4*5/1*2*3*1*2=120/12=10
(x-1) ^5 = x^5-5x^4+10x3-10x2+5x-1
(x+1) ^7
2) Треугольник Паскаля k (1) = 1, k (2) = 7, k (3) = 21, k (4) = 35, k (5) = 35, k (6) = 21, k (7) = 7, k (8) = 1
C0/7=C7/7=1
C1/7=C6/7=7!/1!6!=7
C2/7=C5/7=7! (5!2!) = 1*2*3*4*5*6*7/1*2*3*4*5*1*2=5040/240=21
C3/7=C4/7=7!/3!2!=1*2*3*4*5*6*7/1*2*3*4*1*2*3=5040/144=35
x^7+7x^6+21x^5+35x^4+35x^3+21x^2+7x+1