|ÜêÆÚØ1nÙ‰Y

5·35·( 2)13= C5·35·213,2.x5y13 Xê´µC1818

8·38·( 2)10=C5·38·210.x8y10 Xê´µC1818

nnnn1n+1n+1n+13(2). ª >=[(n+1)++++0123

nn+1···+]n n+1n+1n+1n+11=[++···++]12nn+11(2n+1 1)==m>8. m

=

m(m 1)(m 2)

,3

m m1∴a2

=

m(m 1)

,=m,

+b

m

+c

m

=a

m(m 1)(m 2)

m3

21

3+b am2+2a 3b+6cm,=am+b

m(m 1)

+cm

1

b a=0,2a 3b+6c=0,∴a=1,∴a=6,b=6,c=1,13+23+···+n3

=[(6+632

nnn(6+6+)]

321

12n12n=6(++···+)+6(++···+)+

333222 12n

···+(++···+)

111 n+1n+1n+1=6+6+

432 n+2n+1=6+

42

=

n2(n+1)2 1 1

1222+)+(6+6+)+···+

1321

10.(1)y²µ Ý n iÎG¥§0Ñyóêg iÎG ê f(n) §ÑyÛêg iÎG ê g(n) §@o§k

f(n)=g(n 1)+2f(n 1)=3n 1 f(n 1)+2f(n 1)=3n 1+f(n 1),

n 1 1)+2=3n+1(3f(n)=3n 1+3n 2+···+31+f(1)=3(2) ª > ±n) Ý Ý n iÎG¥§0Ñyóê

g iÎG êoÚ§=Ó1(1)¯"

15. >=

n 1

+

n 1

n 3

kk 1k

n 2n 2n 1n 3=++

kk 1k 1k n 3n 3n 2n 1n 3=+++

kk 1k 1k 1k=m>16. ª===

m1

m2m3

s=

t

=

r,s,t≥0r+s+t=n

r,s,t≥0r+s+t=n

n s t

m3m1+m2

n t

t

m1+m2+m3

n

nnkn

18.y²µ∵(1+x)=k=0x,

k ªü>Ó ¦ , µ

nnk 1n 1

=k=0kn(1+x)x,

k

nnkn 1

x,nx(1+x)=k=0kkü>2g¦ §Ó x=1µ >=n(n+1)2n 2,

m>=,

n

k=1k

2nk

∴y..