Find the sum of the following infinite geometric series, if it exists. 2/5 + 12/25 + 72/125 + ...

1 Answer

llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

for this series `r=(12/25)/(2/5)=(72/125)/(12/25)=6/5=1.2` which is greater than 1.

So, as n increases, the nth term becomes larger and larger and the sum, `S_n` becomes infinite.

It is said that in this case, the geometric series diverges.