Sorry but isn't this statement obvious? If all terms in the a series are less than the terms in the b series, then surely the a series must be smaller than the b series...
I have some issues with this problem.
Let (the sum of an from n=1 to infinity) and (the sum of bn from n=1 to infinity) be two convergent series. If an (less than or equal to) bn for all n in Natural Number, and am < bm for some m in Natural Number, show that (the sum of an from n=1 to infinity) < (the sum of bn from n=1 to infinity).
Well, ish, but a lot of the elementary analysis I'm dealing with seems to be proving somewhat obvious things with a more roundabout method. I mean, if a problem like this came up on the test, I couldn't really just state the statement is self-explanatory. But for me, I have more of an issue of figuring out how to start my proofs.
Well I guess you could argue that a_n will in at least once instance be less than b_n, and then will never possibly exceed or equal b_n, therefore the sum is smaller... depends what kind of arguments you are allowed to use.