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1 solution
A series is diverging when its terms are constantly increasing/staying the same thing.We observe this series at different values.At 1 we get (1+1)^1/1!=2.For 2 we get (2+1)^2/2!=4.5.For 10 we get (10+1)^10/10! whose value I will not show here but you can calculate it and see it is quite big.If you need more proof you can observe more values or come up with formula for increase.