How do you find the sum of the infinite geometric series 7+6+(36/7)+(216/49)+...?

Nov 8, 2015

If the common ratio is $< 1$, then the geometric series will converge

Explanation:

For this problem, the common ratio (r) $= \frac{6}{7}$ which is $< 1$

geometric sum = (first term) $/ \left(1 - r\right)$

geometric sum $= \frac{7}{1 - \frac{6}{7}} = 49$

hope that helped