求1+3/2^2 +4/2^3 +68+n/2^(n-1) +(n+1)/2^n 的值.
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求1+3/2^2 +4/2^3 +68+n/2^(n-1) +(n+1)/2^n 的值.
求1+3/2^2 +4/2^3 +68+n/2^(n-1) +(n+1)/2^n 的值.
求1+3/2^2 +4/2^3 +68+n/2^(n-1) +(n+1)/2^n 的值.
等差数列与等比数列混合,用错位相减法.设原式=s,则2s=2+3/2^1+4/2^2+...+n/2^(n-2)+(n+1)/2^(n-1),s=2s-s=2-(n+1)/2^n+(1/2^1+1/2^2+1/2^3+...+1/2^(n-1))=2-(n+1)/2^n+(1-1/2^(n-1))=3-(n+3)/2^n.
3-(n+3)/2^n。