SOLUTION: I need help with my Algebra please. It says tell whether each sequence is convergent or divergent. If it is convergent find it sum. 1. infinite E (2/3)^n n=0 2. infinite E (-

Algebra ->  Sequences-and-series -> SOLUTION: I need help with my Algebra please. It says tell whether each sequence is convergent or divergent. If it is convergent find it sum. 1. infinite E (2/3)^n n=0 2. infinite E (-      Log On


   

Question 250559: I need help with my Algebra please. It says tell whether each sequence is convergent or divergent. If it is convergent find it sum.
1. infinite E (2/3)^n n=0
2. infinite E (-4/11)^n n=0
3. infinite E (5^k+1)/3^k n=0
4. infinite E (3^n-1)/4^n n=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Recall that the series sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29 is convergent if abs%28r%29%3C1 and it diverges otherwise. If it converges, then sum%28a%2Ar%5En%2Cn=0%2Cinfinity%29=a%2F%281-r%29

So for the first problem, let a%2Ar%5En=%282%2F3%29%5En which makes a=1 and r=2%2F3. Because abs%28r%29=abs%282%2F3%29%3C1, this means that sum%28%282%2F3%29%5En%2Cn=0%2Cinfinity%29=1%2F%281-2%2F3%29=1%2F%281%2F3%29=3. Use the same idea for the rest of the problems.