For what r does 3/(n^(2r - 3))3n2r3 converge or diverge?

1 Answer
Nov 10, 2015

For r>=3/2r32 and only for them.

Explanation:

Let alphaα be a real number.
The sequence (1/n^alpha)_(n \in NN^*) converges if and only if alpha >= 0.

Of course, (1/n^alpha)_(n \in NN^*) converges iff (3/n^alpha)_(n \in NN^*) converges...

So, here, the sequence converges iff 2r-3>=0 iff r>=3/2.