
I want to prove this question. But I am helpless. I don't have any clue how to solve this one. Can someone help

I want to prove this question. But I am helpless. I don't have any clue how to solve this one. Can someone help
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Hint:
Work out the inequality $$p(k+1)>p(k)$$ All factors that both sides have in common (a lot) can be striped away.