Sums Of Infinte Series

1. Mar 16, 2009

Juggler123

Decide (with justification) if the following series converges or diverges;

Sum(1,infinty) (2^(n)+3^(n))/(4^(n)+5^(n))

I've tried using the ratio test but I couldn't see that it was helping in any way, should I be using a different type of test for this problem? I really can't see where to start with this one.

2. Mar 16, 2009

Dick

Try and think of a clever comparison to which you can apply the ratio test. E.g. (2^n+3^n)/(4^n+5^n)<=(3^n+3^n)/(4^n+4^n). See, I substituted a larger numerator and a smaller denominator?

3. Mar 16, 2009

Juggler123

So if you apply the ratio test to the (3^(n)+3^(n))/(4^(n)+4^(n)) you find that this series converges as l<1 (l=3/4?). Is it then allowable to say that the original series converges as it is less than (3^(n)+3^(n))/(4^(n)+4^(n)) and therefore the limit must be lees than the limit of the above series and hence it must converge.

4. Mar 16, 2009

Dick

You tell me, ok? Look up the comparison test for series and make sure all the requirements are fulfilled. It's good practice.