"Suppose are convergent. Let and let converge. Prove that "

I can't make any headways. Any hints would be appreciated.

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- Mar 16th 2006, 06:15 PMTreadstone 71Series
"Suppose are convergent. Let and let converge. Prove that "

I can't make any headways. Any hints would be appreciated. - Mar 16th 2006, 06:28 PMThePerfectHackerQuote:

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. - Mar 16th 2006, 07:24 PMTreadstone 71
The last step is definately not equal. On one side you have n^2 terms, on the other, you have 1+2+3+...+n terms.