4、梅加强参考解答--295页 文字版.pdfVIP

n

22

P(x),kP(k+1)−P(k)=k.k

k=1

32

P(x)=Ax+Bx+Cx+D

2

P(k+1)−P(k)=3Ak+(3A+2B)k+A+B+C

P(k+1)−P(k)=k2

1







3A=1A=





3

3A+2B=0⇒B=−1

2







1





A+B+C=0C=

6

111

32

P(x)=x−x+x+D,D∈R.

326

nn

2

k=[P(k+1)−P(k)]=P(n+1)−P(1)

k=1k=1

1111

32

=(n+1)−(n+1)+(n+1)=n(n+1)(2n+1)

3266

n

k3

k=1

P(x)P(k+1)−P(k)=k3

432

P(x)=Ax+Bx+Cx+Dx+E

32

P(k+1)−P(k)=4Ak+(6A+3B)k+(4A+3B+2C)k