SOLUTION: Determine whether the series 3 - 1 + 1/3 - 1/9 + ... is convergent or divergent. If convergent, find its sum.

Algebra ->  Sequences-and-series -> SOLUTION: Determine whether the series 3 - 1 + 1/3 - 1/9 + ... is convergent or divergent. If convergent, find its sum.      Log On


   



Question 849383: Determine whether the series 3 - 1 + 1/3 - 1/9 + ... is convergent or divergent. If convergent, find its sum.
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
3 - 1 + 1/3 - 1/9 +- ···
That has a%5B1%5D = 3 and r=-1%2F3

It converges since it is a geometric series with |r| < 1

S%5Binfinity%5D%22%22=%22%22a%5B1%5D%2F%281-r%29

S%5Binfinity%5D%22%22=%22%223%2F%281-%28-1%2F3%29%29

S%5Binfinity%5D%22%22=%22%223%2F%281%2B1%2F3%29

S%5Binfinity%5D%22%22=%22%223%2F%281%2B1%2F3%29%22%22%2A%22%223%2F3%22%22=%22%229%2F%283%2B1%29%22%22=%22%229%2F4

Edwin