Question

What is the sum of the infinite geometric series `sum_(n=1)^oo6(0.9)^(n-1)` ?

Answer 1

This is a geometric series with first term 6 and common ratio 0.9 (see geometric series ).
The common ratio is less than 1 in absolute value, so that the series is convergent and its sum is given by `"first term"/(1-"common ratio")=6/(1-0.9)=60`