Question

Find 1/2 + 1/3^2 + 1/2^3 + 1/3^4 + 1/2^5 + 1/3^6.......∞​

Answer 1

Step-by-step explanation:

Separate both geometric series

$(\frac{1}{2} + \frac{1}{ {2}^{3}} + \frac{1}{ {2}^{5} } + ...) +(\frac{1}{ {3}^{2} } + \frac{1}{ {3}^{4} }{ + \frac{1}{ {3}^{6} } } + ...) \: \\ = \frac{ \frac{1}{2} }{1 - { (\frac{1}{2} )}^{2} } + \frac{ {( \frac{1}{3} )}^{2} }{1 - {( \frac{1}{3} )}^{2} } \\ = \frac{19}{24}$