菜乌
幼苗
共回答了20个问题采纳率：90% 举报
A(n+1) - A(n) = 2^n,
A(n) - A(n-1) = 2^(n-1),
...
A(2) - A(1) = 2^(1)
A(n+1) - A(1) = 2^1 + 2^2 + ...+ 2^(n-1) + 2^n = 2[1 + 2 + ...+ 2^(n-1)] = 2[2^n - 1]/[2-1] = 2[2^n-1],
A(n+1) = A(1) + 2[2^n - 1] = 3 + 2^(n+1) - 2 = 2^(n+1) + 1,
A(n) = 2^n + 1.n = 1,2,...
1年前
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