Question

数列0.6+0.66+0.666+0.6666...的前十项和

Answer 1

an=0.6+0.06+……+6*10^(-n)=0.6*(1-0.1^n)/(1-0.1)=2/3-2/3*0.1^n

所以Sn=2/3*n-2/3*(0.1+0.01+……+0.1^n)

=2/3*n-2/3*0.1(1-0.1^n)/(1-0.1)

所以S10=179/27+2/27*0.1^10