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求和k/(2^k).(k=1,2...)
题目详情
求和 k/(2^k) .(k=1,2...)
▼优质解答
答案和解析
S = 1/2 + 2/2^2 + 3/2^3 + 4/2^4 + ...
= 1/2 + 1/2^2 + 1/2^2 + 1/2^3 + 2/2^3 + 1/2^4 + 3/2^4 + .
= 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + .+ (1/2)(1/2 + 2/2^2 + 3/2^3 + ...)
= (1/2) / (1-1/2) + (1/2)S
S - (1/2)S = 1
S = 2
Answer 2
= 1/2 + 1/2^2 + 1/2^2 + 1/2^3 + 2/2^3 + 1/2^4 + 3/2^4 + .
= 1/2 + 1/2^2 + 1/2^3 + 1/2^4 + .+ (1/2)(1/2 + 2/2^2 + 3/2^3 + ...)
= (1/2) / (1-1/2) + (1/2)S
S - (1/2)S = 1
S = 2
Answer 2
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