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User:Matt Kwan/Sandbox

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At this stage was shown to be less than or equal to which is correct but if this is done the conclusion of the proof is:



will increase without bound if , so this method does not prove the general case that is bounded. (When there is a divide-by-zero problem as well.)


A possible although unwieldy solution is to replace k! with something other than . I propose a complete solution as follows:


(using as the ceiling function):



therefore:



is a GP, so using with as the number of terms and as the growth per term:



But for all :



So


therefore:



which is a bound independent of