How to Determine Whether a Sequence is Increasing or Decreasing by Using Calculus

How to Determine Whether a Sequence is Increasing or Decreasing by Using Calculus

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[JAKE-ngyr]

but why is it increasing? a1 will be for example 17/15 but a2 will be 17/30 a3 17/45 and so on. So how is it increasing

[jamesradcliff]

What about the sequence a_n = 1 + 1/n? If you set the function equal to f(x) and take the derivative, you get f(x) = -1/x^2. This function is negative so you would expect that it is decreasing for x ≥ 1, but if you graph the function from x = 1 onwards in the positive direction, it looks like it is increasing. Why is that?

[gatorscoops]

can't we just use l'hospital's rule for the derivative for the fraction?