Question

what is the sum of the infinite geometric series 1/3+2/15+4/75+...

Answer 1

a=1/3
\[r=\frac{ 2 }{15 }\div \frac{ 1 }{3 }=\frac{ 2 }{15 }\times \frac{ 3 }{ 1 }=\frac{ 2 }{ 5 }\]
here r=2/5<1
\[s \infty=\frac{ a }{1-r }\]
\[ s=\frac{ \frac{ 1 }{ 3} }{\frac{ 2 }{5 } }=\frac{ 1 }{3 }\times \frac{ 5 }{ 2 }=\frac{ 5 }{ 6 }\]

Answer 2

5/6 is not the answer