Question: Evaluation of a sum

Hi all, 

I am stuck in the follow sum:

Write a procedure to evaluate the sum of Sn and use this to find the value of n=10^p, p=1,2,3,4,5.

I started with defining Sn, 

restart:
Sn:=sum((1/k^(1/10))*sin(1/k), k=1..n);

Perhaps sum is not the correct one? Perhaps add?

And help appreciated

 

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