Question
what does this series, if it converges, converge to?
the series from n=1 to infinity of
(2^n + (-1)^n)/3^n
the series from n=1 to infinity of
(2^n + (-1)^n)/3^n
Answers
drwls
It looks like that can be written as the sum of two series:
(2/3)^n and (-1/3)^n
Use the fact that the sum of the series from 1 to infinity r^n = 1/(1-r) , for |r|<1
That makes the limit 1/(1/3) + 1/(4/3)
= 3 3/4
(2/3)^n and (-1/3)^n
Use the fact that the sum of the series from 1 to infinity r^n = 1/(1-r) , for |r|<1
That makes the limit 1/(1/3) + 1/(4/3)
= 3 3/4