You can write it like this
IEnumerable<int> range = Enumerable.Range(1, n);
var sum = range.Aggregate(0, (x, y) => x + y);
Sum of squares:
IEnumerable<int> range = Enumerable.Range(1, n);
var sum = range.Aggregate(0, (x, y) => x + y * y);
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solved How to use self defined aggregate function with LINQ? (without using extension methods)