Let be a convergent series.

Let , .

Let be a sequence such that .

Prove that is convergent.

---------

I see here that

looks like the ratio test.

has upperbound M.

How do I go about this proof?

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- Nov 3rd 2009, 11:42 AMflipperpkconceptual summation problem
Let be a convergent series.

Let , .

Let be a sequence such that .

Prove that is convergent.

---------

I see here that

looks like the ratio test.

has upperbound M.

How do I go about this proof? - Nov 3rd 2009, 12:03 PMJameson
There is already a proof about this situation:

Abel's test - Wikipedia, the free encyclopedia

The only thing lacking is b_n being monotonic, but somehow I think that's assumed. - Nov 3rd 2009, 12:43 PMgirdav
We have