f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 20:29:40
f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?
x)KӴ567bc=== gaciiFqچ fMR> l(QV(bD;P@46ty 4a,#M,X -Vu# .P_.g_\g8rfJ

f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?
f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?

f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?
∵f(2^k)=1+1/2+...+1/2^k,
f(2^(k+1))=1+1/2+...+1/2^k+1/(2^k+1)+1/(2^k+2)+...+1/2^(k+1)
∴f(2^(k+1))-f(2^k)=1/(2^k+1)+1/(2^k+2)+...+1/2^(k+1)[共2^(2+1)-2^k=2^k项].