Appendix A
A.1
1
0
(1)
k
kk r
r
k
nn n
r
−
=
⎛⎞
+−=⎜⎟
⎝⎠
∑
1
0
(1) (1)
k
kk r
r
k
nn n
r
−
=
⎛⎞
−− = −
⎜⎟
⎝⎠
∑
“
A.2 for 3k= 3
333
(,0) (,1) (,2) ( 1) 1
012
Sn Sn Sn n
⎛⎞ ⎛⎞ ⎛⎞
++ =+=
⎜⎟ ⎜⎟ ⎜⎟
⎝⎠ ⎝⎠ ⎝⎠
3
(1)
33[(,2)](1)1
nn
nSnn
+
⎡⎤
++=+−
⎢⎥
for k = 4 4
4444
(,0) (,1) (,2) (,3) ( 1) 1
0123
Sn Sn Sn Sn n
⎛⎞ ⎛⎞ ⎛⎞ ⎛⎞
+++=+−
⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟
⎝⎠ ⎝⎠ ⎝⎠ ⎝⎠
4
(1) (1)(21)
46 4(,3)(1)1
22
nn nn n
nSnn
+++
+⋅ +⋅ + = + −
Appendix A 259
42
432 2 32
1
5 ( , 4) [6( 1) 6 15 10 (2 1) 15 ( 1)]
6
1[6 24 36 24 6 6 15 20 10 15 15 ]
6
n
Sn n n n n n n
nnnnn nnnnn
+
⋅= +−−− +−+
+
= + + + +−− − − − −
A.3 (a) 13(2)4(1)212 10x=++− ++− +++ =
∑
(b) 2194161414 40x=+ + + ++ ++ =
∑
A.4 (a) 34567 25x=++++=
∑
(b) 371052 27f=++ ++=
∑
(c) 928503014131xf =++++=
∑
(d) 227 112 250 180 98 667xf=+ + + +=
∑