(a) Let n be a positive integer greater than 2. Show that 1 1 +...+ 1 < In n <1+ 2 1 + 1 2 3 n-1 (Hint: compute the lower and upper sum of given the partition P = {1,2, 3, ...,n}.) (b) Use the result above to show the divergence of harmonic series, i.e. the sum 1. 1 1++ 1 1 +-+:+ 3 4 is infinite. (Hint: it suffices to show given any M > 0, there exists a positive integer n such that 1+++ .+ > M.)

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