Question 175168
The sequence that generates  1, 1/5, 1/25, 1/125,... is {{{a[n]=(1/5)^n}}}. Take note that the sequence is in the form {{{a[n]=a*r^n}}} where {{{a=1}}} and {{{r=1/5}}}.



Remember, the formula for the sum of an infinite series is


{{{S=a/(1-r)}}}



{{{S=1/(1-1/5)}}} Plug in {{{a=1}}} and {{{r=1/5}}}



{{{S=1/(4/5)}}} Subtract



{{{S=5/4}}} Invert the fraction and multiply



So the answer is {{{S=5/4}}} which means that 1+1/5+1/25+1/125+...=5/4