- #1

kingwinner

- 1,270

- 0

_{k}be a series with positive terms.

__Ratio test:__

Suppose a

_{k+1}/a

_{k}-> c.

If c<1, then ∑a

_{k}converges.

If c>1, then ∑a

_{k}diverges.

If c=1, the test is inconclusive.

What if a

_{k+1}/a

_{k}diverges (i.e. a

_{k+1}/a

_{k}->∞)? Do we count this as falling into the case c>1? Can we say whether ∑a

_{k}converges or not?

__Root test:__

Suppose limsup (a

_{k})

^{1/k}= r.

If r<1, then ∑a

_{k}converges.

If r>1, then ∑a

_{k}diverges.

If r=1, the test is inconclusive.

What if limsup (a

_{k})

^{1/k}= ∞? Do we count this as falling into the case r>1? Can we say whether ∑a

_{k}converges or not?

Thanks for clarifying!