Question 777820
{{{1+r+r^2+" ...+"r^(n-1)=(1-r^n)/(1-r)}}}
 
{{{n=2}}} --> {{{1+r^(2-1)=1+r=(1-r^2)/(1-r)}}}
 
{{{n=k}}} --> {{{1+r+r^2+" ...+"r^(k-1)=(1-r^k)/(1-r)}}}
{{{1+r+r^2+" ...+"r^(k-1)+r^k=(1-r^k)/(1-r)+r^k}}}
{{{1+r+r^2+" ...+"r^(k-1)+r^k=(1-r^k)/(1-r)+r^k(1-r)/(1-r)}}}
{{{1+r+r^2+" ...+"r^(k-1)+r^k=(1-r^k)/(1-r)+(r^k-r^k+1)/(1-r)}}}
{{{1+r+r^2+" ...+"r^(k-1)+r^k=(1-r^k+r^k-r^k+1)/(1-r)}}}
{{{1+r+r^2+" ...+"r^(k-1)+r^k=(1-r^k+1)/(1-r)}}}