Hint $1.$ You do not need Decimal$()$ in this problem. Some of you will try to use it$,$ but it's not necessary. In fact, using it is likely to generate "out$-$of$-$memory" errors.

Hint $2.$ Some of you will try to "implement" the error formula to somehow compensate for the round$-$off error. But that shouldn't make sense to do$.($Why not? Because the formula above is a bound, not an exact formula.$)$ Instead, the intent of this problem is to see if you can look at the formula and understand how to interpret it$.$ That is$,$ how does the formula tell you to perform the summation to make it more accurate than the conventional method?

Hint $3.$ Some of you will look up fancy algorithms to compensate for error. That's great, because you may learn something deep in the process, but it's also not necessary. Again, see Hint $2.$

Note. The test cell will disallow certain "shortcuts" on this problem, namely, importing certain implementations of summation. Only basic Python is needed.