Define $$S=\sum _{r=1}^n a_r$$
How to prove the following inequality: $$\prod _{r=1}^n (1+a_r)\leq \sum _{r=0}^n \frac{S^r}{r!}$$
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Welcome to MSE. Please see https://math.stackexchange.com/help/notation for how to properly render math here, instead of giving a link to the problem, which is strongly depreceated. – macton Jan 23 '21 at 10:59
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1Are you sure this is true and there is no condition on $a_r$ ? – SagarM Jan 23 '21 at 11:36
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There should be some sort of condition. If we take $a_1 = a_2 = \ldots = a_n = 0$, then S = 0 and we get $1 \le 0$ which is absurd. – Oussema Jan 24 '21 at 22:20
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@Oussema Your argument requires to reject $0^0 / 0! = 1$. – Andreas Jan 25 '21 at 15:39
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Does this answer your question? : The answer by @coffeemath at: https://math.stackexchange.com/a/485552/317854 – Andreas Jan 25 '21 at 15:48