已知数列{an}满足a1=254，an+1−an=2n，当n=时，ann取得最小值．

Question

已知数列{a_n}满足a₁=(25)/(4)，an+1−an=2n，当n=______时，(an)/(n)取得最小值．

Answer 1

因为a1＝254，an+1−an＝2n，所以an=an-1+2（n-1）=an-2+2（n-2）+2（n-1）=an-3+2（n-3）+2（n-2）+2（n-1）=…=a1+2×1+2×2+…+2（n-1）=254+2×(n−1)[1+(n−1)]2=254+n2-n．∴ann=254n+n-1≥2254n•n-1，当254n...