個(gè)性化學(xué)習(xí)
來源:學(xué)大教育 時(shí)間:2013-12-21
已知等差數(shù)列{an}的公差d不等于0,且a1,a3,a13成等比數(shù)列,
若a1=1,,Sn是數(shù)列{an}前n項(xiàng)的和,則(2Sn+16)/(an+3)
(n不屬于N*)的最小為
解:a3²=a13*a1=a13
a3=a1+2d=1+2d
a13=a1+12d=1+12d
(1+2d)²=1+12d
1+4d+4d²=1+12d
4d²-8d=0
d=0舍去,d=2
an=2n+1
Sn=n²
(2Sn+16)/(an+3)
=(2n²+16)/(2n+1+3)
=(n²+8)/(n+2)
是單調(diào)增加函數(shù),當(dāng)n=1時(shí),有最小值3