Direct comparison test is applicable when `suma_n` and`sumb_n` are both positive sequences for all n, such that `a_n<=b_n` .It follows that:

If `sumb_n` converges then `suma_n` converges.

If `suma_n` diverges then `sumb_n` diverges.

`sum_(n=1)^oo1/(2n-1)`

Let `b_n=1/(2n-1)` and `a_n=1/(2n)`

`1/(2n-1)>1/(2n)>0` for `n>=1`

As per p series test `sum_(n=1)^oo1/n^p` is convergent if `p>1` and...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

Direct comparison test is applicable when `suma_n` and`sumb_n` are both positive sequences for all n, such that `a_n<=b_n` .It follows that:

If `sumb_n` converges then `suma_n` converges.

If `suma_n` diverges then `sumb_n` diverges.

`sum_(n=1)^oo1/(2n-1)`

Let `b_n=1/(2n-1)` and `a_n=1/(2n)`

`1/(2n-1)>1/(2n)>0` for `n>=1`

As per p series test `sum_(n=1)^oo1/n^p` is convergent if `p>1` and divergent if `p<=1`

`sum_(n=1)^oo1/(2n)=1/2sum_(n=1)^oo1/n`

`sum_(n=1)^oo1/n` is a p-series with p=1, so it diverges.

Since `sum_(n=1)^oo1/(2n)` diverges ,the series `sum_(n=1)^oo1/(2n-1)` diverges too by the direct comparison test.