proof of absolute convergence theorem
Suppose that is absolutely convergent, i.e., that is convergent. First of all, notice that
and since the series has non-negative terms it can be compared with and hence converges.
On the other hand
Since both the partial sums on the right hand side are convergent, the partial sum on the left hand side is also convergent. So, the series is convergent.
|Title||proof of absolute convergence theorem|
|Date of creation||2013-03-22 13:41:52|
|Last modified on||2013-03-22 13:41:52|
|Last modified by||paolini (1187)|