帮忙做做这道数学题已知等差数列{an}的前n项和为Sn,且a3=10,a5=18.(1)求Sn;(2)令bn=Sn/n,
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帮忙做做这道数学题
已知等差数列{an}的前n项和为Sn,且a3=10,a5=18.(1)求Sn;(2)令bn=Sn/n,求f(n)=(n+9)·bn+1/bn(n€N^*)的最小值. (注:题中/为分号)
已知等差数列{an}的前n项和为Sn,且a3=10,a5=18.(1)求Sn;(2)令bn=Sn/n,求f(n)=(n+9)·bn+1/bn(n€N^*)的最小值. (注:题中/为分号)
![帮忙做做这道数学题已知等差数列{an}的前n项和为Sn,且a3=10,a5=18.(1)求Sn;(2)令bn=Sn/n,](/uploads/image/z/2530179-27-9.jpg?t=%E5%B8%AE%E5%BF%99%E5%81%9A%E5%81%9A%E8%BF%99%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94a3%3D10%2Ca5%3D18.%281%29%E6%B1%82Sn%3B%282%29%E4%BB%A4bn%3DSn%2Fn%2C)
1.a3=a1+2d=10 a5=a1+4d=18 两式相减:2d=8 ,d=4 ,a1=2 Sn=na1+[n(n-1)d/2]=2n^2 2.bn=Sn/n=2n^2/n=2n f(n)=(n+9)[2(n+1)]/2n =n^2+10n+9 /n =n+(9/n)+10≥10+√[n×(9/n)]=13 当切仅当n=9/n ,即n=3时,f(n)最小值为13.
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