Wednesday, 11 March 2015

real analysis - Let f:[0,infty)to[0,infty) be a continuous function such that $int_0^{infty} f(t) dt

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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