4+0.44+0.444+~+0.44444.4

问题描述:

4+0.44+0.444+~+0.44444.4

an=4/9*(10^n-1)*10^(-n)=4/9(1-1/10^n)
Sn=4/9[n-(1/10+1/10^2+...+1/10^n)]
=4/9[n-1/10(1-1/10^n)/(1-1/10)]
=4/9[n-1/9*(1-10^(-n)]