Chapter 11 - Further Topics in Algebra - 11.3 Geometric Sequences and Series - 11.3 Exercises - Page 1035: 63

$\dfrac {3}{4}$

$\sum ^{\infty }_{i=1}\left( \dfrac {3}{7}\right) ^{i}=\dfrac {a_{1}}{1-r};a_{1}=\left( \dfrac {3}{7}\right) ^{1}=\dfrac {3}{7};r=\dfrac {3}{7}\Rightarrow S_{\infty }=\dfrac {\dfrac {3}{7}}{1-\dfrac {3}{7}}=\dfrac {3}{4}$