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f(n)=1/2+1/3+1/4...+1/(2^n-1),则f(k+1)-f(k)=
题目详情
f(n)=1/2+1/3+1/4 ...+1/(2^n-1) ,则f(k+1)-f(k)=
▼优质解答
答案和解析
f(k+1)有2^(k+1)-2项,f(k)有2^k-2项
因此f(k+1)-f(k)有[2^(k+1)-2]-[2^k-2]=2^k项,即
f(k+1)-f(k)=1/2^k+1/(2^k+1)+.+1/(2^(k+1)-2)+1/(2^(k+1)-1)
因此f(k+1)-f(k)有[2^(k+1)-2]-[2^k-2]=2^k项,即
f(k+1)-f(k)=1/2^k+1/(2^k+1)+.+1/(2^(k+1)-2)+1/(2^(k+1)-1)
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