I think that there is no other logical choice than is as an answer in this instance. Why? As stated, the sentence uses the singular form of the noun source, not the plural -- sources. I have never come across this idea of cutting down a compound subject that would govern the plural verb as complement. It intuitively would read like this:
Ample knowledge and a rich accumulation of life experience __are___ the major sources of a sense of humor.
In fact, a strict analysis should discount ignoring the nature of the subject 'knowledge and accumulation' as truly a compound subject and matching it to a singular noun 'source.' A compound subject not only governs the plural in predicate, it also is generally not ignored for its compound nature.
There are exceptions to this simplistic analysis just cited. For instance, if the conjunction connecting the two nouns were "or" instead of "and," then the singular "is" would be definitely correct.
I suppose the reasoning for choosing "is" would have to be that "A" rich accumulation of life experience is singular in its aspect and can therefore be matched by the singular of the verb to be -- "is." However, I would never use this construction myself unless someone could show me a reference. I was so puzzled that I found such a reference, and here it is for you, but I give you fair warning -- it won't give clear sanction either. It is: http://www.learnersdictionary.com/qa/compound-subjects-and-verb-number
I do think you will receive good instruction from it. This question caught my eye.