First of all I'd like to say that infinity is not a number, so you cannot make mathematical calculations with it. It's no more valid to say what is f(infinity) than it is to say what is f(Michael). It just doesn't make sense.
Second of all, since you say there are infinity seeds that will be planted, that automatically messes up the problem not only because of the above stated reason but because the bird will never catch up with eating the seeds if the farmer never stops.
Third of all, adding in a factor of time by saying it takes 2 seconds to complete the process doesn't change a thing. All it does is direct one towards thinking finitely because the event seems to have an end in time [But as far as the process goes those 2 seconds are eternity. You can probably find theory on this if you search the web but the reason this is so is you must divide (remember this is invalid, because you cannnot use any functions of infinity) the period of time into infintesimally small units to express the time it took to plant one seed after another] when it actually does not [in fact, associating the word infinity with something like time or space is invalid, because it cannot exist in time or space. The only thing infinite is God, who is not limited by spacetime, that is why God is eternal (it is more accurate to say God is beside time began than before time began), in fact he created time itself (and everything else for that matter). So numbers (limited) are entirely different from infinity (unlimited). To fully grasp infinity and eternity, wait until you die and reach eternal life/death. You'll definitely understand it all then and so will I (I'm just stating the theory)
Fourth of all, since the farmers never stop planting, saying after they finish simply doesn't make sense. When you add the quotes: '"finish"' you must mean at any given point in the process of planting (in which case there would be the same amount of seeds on the ground for each farmer). So far all this would be resolved by saying the farmers plants, for example, a 100 long row of seeds. It is illogical to say it is never ending [they must be doing it in eternity (heaven/hell) to have a limitless amount of what we would understand as space and time to do this]
Fifth of all, there is only one tenth seed
just like there's only one first seed (well, ok I guess it could literally mean what you wanted it to mean as well)
Sixth of all the word eventually doesn't make sense in the context (not too dificult to figure out)
Seventh of all if for example they were doing 100 long rows of seed, each would have the same amount of seeds at the end if they simply replaced the seeds the birds ate
And finally, if for example they were 100 long rows of seed there should be 90 seeds left for farmer A and 9 seeds left for farmer B (unless the birds pooped the seeds back on the ground