Answer some calculus math problems on power series

It's clear with 10. Sum[n(x+5)^(2n-1)/(n-2)!], n=2,3,... But I don't see in the picture what I must do in 12,16.

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Hi, I am University professor of Mathematics. I have great knowledge in the topic you need help. I guarantee 100% correct solutions and detailed explanations. For example the solution for the question 12 is 1/(1-5x) and it is valid for |x|<1/5.

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