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Senior one mathematics collection problem.
Method 1.

The value of the sum of all pks.

= (-5 + 1)*(-4 + 1)*(-3 + 1)*...*(5+ 1) - 1

= - 1

Note: Each factor in the above formula is the value of an element plus 1.

If you expand all the above formulas without merging, you will get all pk. However, an additional item 1* 1*...* 1 corresponds to an empty set and should be deleted. So subtract 1.

Method two.

The subset either contains-1 or does not. For each subset with-1, delete-1 to get a subset without-1. (The only exception is the subset containing-1 {- 1}), and each subset pi without-1 is added with the element-1 to get a subset pj containing-1. Note that pj = -pi.

So the value of the sum of all pks = the product of all elements in the subset {-1} containing only-1=-1.