设数列an满足a1=2 an+1-an=3-2^2n-11.求数列的通项 2.令bn=n*an 求数列bn的前N项和
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设数列an满足a1=2an+1-an=3-2^2n-11.求数列的通项2.令bn=n*an求数列bn的前N项和设数列an满足a1=2an+1-an=3-2^2n-11.求数列的通项2.令bn=n*an
设数列an满足a1=2 an+1-an=3-2^2n-11.求数列的通项 2.令bn=n*an 求数列bn的前N项和
设数列an满足a1=2 an+1-an=3-2^2n-1
1.求数列的通项
2.令bn=n*an 求数列bn的前N项和
设数列an满足a1=2 an+1-an=3-2^2n-11.求数列的通项 2.令bn=n*an 求数列bn的前N项和
(1)根据题意,有An=(An-An-1)+(An-1 - An-2)+…+(A2 - A1)+A1
=3-2^(2n-3) + 3-2^(2n-5) +…+(3-2^3)+ 2
再用分组求和法:
=3n - 【2^(2n-3)+2^(2n-5)+…2^3+2】
=3n-2*(1-4^n)\(1-4)
=2*(1-4^n)\3 + 3n
即An=-2*(4^n-1)\3 + 3n
(2)Bn=n*An==-2n*(4^n-1)\3 + 3n^2
与(1)同理:用分组求和法
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