求一道数学题，谢谢各位高手帮忙，好的话有加分

易知：
f(1)+f(2)+f(3)+……+f(n-1)+f(n)
=1+1+1/2+1+1/2+1/3+……+1+1/2+1/3+……+1/n
=n+(n-1)/2+(n-2)/3+……+1/n
=n+n/2+n/3+……+n/n-[1/2+2/3+……+(n-1)/n]
=n*(1+1/2+1/3+……+1/n)-(1-1/2+1-1/3+……+1-1/n)
=nf(n)-[n-1-f(n)+1]
=nf(n)+f(n)-n
故f(1)+f(2)+f(3)+……+f(n-1)=nf(n)-n
=n[f(n)-1]
故g(n)=n

f(1)+f(2)+f(3)+……+f(n-1)+f(n)
=1+1+1/2+1+1/2+1/3+……+1+1/2+1/3+……+1/n
=n+(n-1)/2+(n-2)/3+……+1/n
=n+n/2+n/3+……+n/n-[1/2+2/3+……+(n-1)/n]
=n*(1+1/2+1/3+……+1/n)-(1-1/2+1-1/3+……+1-1/n)
=nf(n)-[n-1-f(n)+1]
=nf(n)+f(n)-n
故f(1)+f(2)+f(3)+……+f(n-1)=nf(n)-n
=n[f(n)-1]
故g(n)=n