Note:C(n,r) = nCr=n!/(n-r)!r!
(a)
By considering the expansion of (1+x)^n and (1+x)^(n+2)
show C(n+2, r+2)=2C(n,r+1)+C(n, r+2)
(b)
show(n+2)! /x(x+1)(x+2)....(x+n+2)= summation r from 0 to (n+2) (-1)^r C(n+2,r) / (x+r)
(c)
use the above, show
(n+2)!/ 2x(x+1)(x+2).....(x+n+2)=C(n,0)/x(x+1)(x+2)- C(n,1)/(x+1)(x+2)(x+3)+...+
(-1)^n C(n,n)/(x+n)(x+n+1)(x+n+2)
更新1:
sorry, (a) is By considering the expansion of (1+x)^n and (1+x)^(n+2) show C(n+2, r+2)= C(n,r)+ 2C(n,r+1)+C(n, r+2) for 0
更新2:
sorry, (a) is By considering the expansion of (1+x)^n and (1+x)^(n+2) show C(n+2, r+2)= C(n,r)+ 2C(n,r+1)+C(n, r+2) for 0
更新3:
我都無計喇, 學校考試出左,我想知番點做, 求証一下姐! E次考試好深, 個個都無佢收!