Let f:[0,∞)→[0,∞) be a continuous function such that ∫∞0f(t)dt<∞
then which of following are true
(1) the sequence {f(n)} is bounded
(2) f(n)→0 as n→∞
(3) the series ∑f(n) is convergent
i think option 1 and 2 is true, and option 3 is false.but not able to prove 1 and 2 and disprove 3.
any hint please
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