How do I solve: Determine whether the series ((1+(2^k))/ ((3^k)-1))?
Determine whether the series ((1+(2^k))/ ((3^k)-1)) CONVERGES OR DIVERGES
- asimovLv 610 years agoFavorite Answer
k=1 , 3/2
k=2 , 5/8
k=3 , 10/26
the serie convergens to the asymptote 2^k/ 3^k = (2/3)^k
and for k-->oo , (2/3)^k =0
couse for every n , |n|<1 it will be convergens to 0
- MathPhDLv 610 years ago
These terms converge to 0, because the terms are positive and dominated by (9/4)(2/3)^k, which go to 0.
If you mean the sum of these terms, then the answer is still that it converges. This is because the sum with these dominating terms is a converging geometric series.