数列与不等式结合证明题.
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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
Cn=[(n+4)(n+5)]/[(n+1)(n+2)].Sn为数列{Cn}的前n项和,证明Sn
![数列与不等式结合证明题.](/uploads/image/z/5640872-32-2.jpg?t=%E6%95%B0%E5%88%97%E4%B8%8E%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%BB%93%E5%90%88%E8%AF%81%E6%98%8E%E9%A2%98.)
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]
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]