求数列3/2,13/4,41/8,113/6,···,((2n-1)*2^n+1)/2^n,···前n项和第四项是113/16,不是113/6,对不起,打错了
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![求数列3/2,13/4,41/8,113/6,···,((2n-1)*2^n+1)/2^n,···前n项和第四项是113/16,不是113/6,对不起,打错了](/uploads/image/z/110531-11-1.jpg?t=%E6%B1%82%E6%95%B0%E5%88%973%2F2%2C13%2F4%2C41%2F8%2C113%2F6%2C%C2%B7%C2%B7%C2%B7%2C%28%282n-1%29%2A2%5En%2B1%29%2F2%5En%2C%C2%B7%C2%B7%C2%B7%E5%89%8Dn%E9%A1%B9%E5%92%8C%E7%AC%AC%E5%9B%9B%E9%A1%B9%E6%98%AF113%2F16%EF%BC%8C%E4%B8%8D%E6%98%AF113%2F6%EF%BC%8C%E5%AF%B9%E4%B8%8D%E8%B5%B7%EF%BC%8C%E6%89%93%E9%94%99%E4%BA%86)
求数列3/2,13/4,41/8,113/6,···,((2n-1)*2^n+1)/2^n,···前n项和第四项是113/16,不是113/6,对不起,打错了
求数列3/2,13/4,41/8,113/6,···,((2n-1)*2^n+1)/2^n,···前n项和
第四项是113/16,不是113/6,对不起,打错了
求数列3/2,13/4,41/8,113/6,···,((2n-1)*2^n+1)/2^n,···前n项和第四项是113/16,不是113/6,对不起,打错了
((2n-1)*2^n+1)/2^n
=[(2n-1)*2^n]/2^n+1/2^n
=(2n-1) + (1/2)^n
则
Sn = [1+(2n-1)]*(2n-1)/2 + 1/2*[1-(1/2)^n]/(1-1/2)
=n*(2n-1) + [1-(1/2)^n]