Show that if n belongs to N, and:

An: = (1 + 1/n)^n

then An < An+1 for all natural n. (Hint, look at the ratios An+1/An, and use Bernoulli's inequality)

I think i have a vague idea of what to do here, like im sure induction is involved in this proof/ However, im unsure how bernoullis inequality and the ratios help in the proof. Can anyone help me please?

An: = (1 + 1/n)^n

then An < An+1 for all natural n. (Hint, look at the ratios An+1/An, and use Bernoulli's inequality)

I think i have a vague idea of what to do here, like im sure induction is involved in this proof/ However, im unsure how bernoullis inequality and the ratios help in the proof. Can anyone help me please?

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