I need to show that this series diverges: n/(2n^2+3) by comparison with: 1/(2n). I think 1/(2n) diverges as it is simply 1/2 time the harmonic series. The problem I have is that my original series simplifies to: 1/(2n+3/n) once divided through by 'n' which is dominated by 1/(2n). I did not think it was possible to show a series diverges by showing a dominant series also diverges. Any advice please?

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sig(n/an2+3)>sig(n/2n2+4n)=sig(1/n+2)=diverge ->sig(n/2n2+3)=diverge

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