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I don't mean to ask without show of any working, but I would like to have some hints, I've tried dividing both sides by (1+h), however, it lead me nowhere.

Any hints as to how I should approach this question?

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Hint: by Bernoulli's inequality:

$$ 1+nh \le (1+h)^n \tag{1} $$

Then, since $0 \le h \le 1\,$:

$$ (1+h)^n(1-h)^n = (1-h^2)^n \le 1 \tag{2} $$

Now multiply $(1)$ and $(2)$ together.

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    Thanks, but we are not suppose to have knowledge such as bernoulli's inequality. Managed to solve it without. – 2017-02-28
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    @user51515 That's precisely why it's a good idea to add some context when you post a question, otherwise no one can guess. `Managed to solve it` You should consider posting that as a self-answer, which is perfectly OK around here. – 2017-02-28