数列与不等式结合证明题.Cn=[(n+4)(n+5)]/[(n+1)(n+2)].Sn为数列｛Cn｝的前n项和,证明Sn
问题描述：
数列与不等式结合证明题.
Cn=[(n+4)(n+5)]/[(n+1)(n+2)].Sn为数列｛Cn｝的前n项和,证明Sn
答
证明：
Cn=[(n+1)+3][(n+2)+3]/[(n+1)(n+2)]
=1+3[1/(n+1)+1/(n+2)]+9[1/(n+1)-1/(n+2)]
=1+6[2/(n+1)-1/(n+2)]
0,f(x)上凹,
有f[(x1+x2)/2]