Question

Question #b6d9b

Answer 1

The sequences are convergent to `0` and the series are divergent.

Explanation:

Considering the series:

For `a,b in RR^+` we have for `n > 1`

`1/(max(a,b)(n-1)) < 1/(an-b)` (supposing that `an-b ne 0`) and we know that

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

So for `n^@ > max(1,floor(b/a))` we have

`1/(max(a,b)) sum_(n = n^@)^oo 1/(n-1) < sum_(n = n^@)^oo1/(an-b)`

but

`sum_(n = n^@)^oo 1/(n-1)` diverges so `sum_(n = n^@)^oo1/(an-b)`

diverges also.