"Suppose are convergent. Let and let converge. Prove that "
I can't make any headways. Any hints would be appreciated.
Perhaps you should look at its partial sums.Originally Posted by Treadstone 71
Let represent the nth partial sum of let represent the nth partial sum of and represent the nth partial sum of .
Thus, if we can show that the partial sums of these two series' are equal then they converge to the same number.
Notice that:
Then,
=
(I might have made a mistake on the last step where I claim it is but I do not see anything wrong)
Q.E.D.