s := \sum_{i=0}^\infty {4+3i \over 5^i}\\
s = \sum_{i=0}^\infty {4+3i \over 5^i} = 4+\sum_{i=1}^\infty {4+3i \over 5^i} \\
= 4 + {1 \over 5}\sum_{i=0}^\infty {4+i+3 \over 5^i} \\
= 4 + {1 \over 5}\sum_{i=0}^\infty {4+i \over 5^i}+3\sum_{i=1}^\infty {1 \over 5^i} \\
= 4 + {1 \over 5}s + {3 \over 5-1} \\
= {1 \over 5}s + {19 \over 4} \\
20s = 4s + 95 \\
s = {95 \over 16}