已知等差数列{an}中,an=4^n-1 +n,n属于n,(1)求数列{an}的前n项和sn(2)证明不等式sn+1小于等于4sn,对任意n属于正整数皆成立
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![已知等差数列{an}中,an=4^n-1 +n,n属于n,(1)求数列{an}的前n项和sn(2)证明不等式sn+1小于等于4sn,对任意n属于正整数皆成立](/uploads/image/z/2681859-3-9.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Can%3D4%5En-1+%2Bn%2Cn%E5%B1%9E%E4%BA%8En%2C%281%29%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8Csn%282%29%E8%AF%81%E6%98%8E%E4%B8%8D%E7%AD%89%E5%BC%8Fsn%2B1%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E4sn%2C%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E5%B1%9E%E4%BA%8E%E6%AD%A3%E6%95%B4%E6%95%B0%E7%9A%86%E6%88%90%E7%AB%8B)
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已知等差数列{an}中,an=4^n-1 +n,n属于n,(1)求数列{an}的前n项和sn(2)证明不等式sn+1小于等于4sn,对任意n属于正整数皆成立
已知等差数列{an}中,an=4^n-1 +n,n属于n,(1)求数列{an}的前n项和sn(2)证明不等式sn+1小于等于4sn,对任意n属于正整数皆成立
已知等差数列{an}中,an=4^n-1 +n,n属于n,(1)求数列{an}的前n项和sn(2)证明不等式sn+1小于等于4sn,对任意n属于正整数皆成立
Sn=4^0+4^1+…+4^(n-1)+1+2+…+n=(4^n-1)/3+n(n+1)/2
S(n+1)=(4^(n+1)-1)/3+(n+1)(n+2)/2
4Sn==(4^(n+1)-4)/3+2n(n+1)
4Sn-S(n+1)=(3n^2+n-4)/2>=0
OK