Prove using algebra that the sequence `(4n) /(n +3)` is increasing.

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degeneratecircle eNotes educator| Certified Educator

I edited the question to say series instead of sequence, since I think that's what you meant (if these were terms in a series, then since they're all positive the series is increasing, which would be the whole proof).

Anyway, if we label the terms of the sequence as `s_n=(4n)/(n+3),` then if we can show that `s_(n+1)-s_n>0` for any `n,` this proves by definition that our sequence is increasing for all `n` .



`=12/((n+4)(n+3))>0,`      (since `n>=0`)

as we wished to show. This finishes the proof. The third sentence in the link describes an alternate method that works for this example.