Express 1000 as a Sum of Consecutive Natural Numbers [Sequence Week #1]

NOTE: At 2:39, (2a+n-1)-n must be 2a-1, not 2a+1. However, 2a-1＞0 still holds when a is natural number.

This week will be the "Sequence Week," in which I am going to upload videos that are related to, well, sequences. I want to open this week with quite fascinating problem. We have to express 1000 as the sum of consecutive natural numbers. Consecutive natural numbers can be considered as an "arithmetic sequence," but it will take more than applying simple formulas related to the arithmetic sequence to solve this problem!

My other videos of the Sequence Week:
- Geometric Sequence: Sum vs. Product vs. Reciprocal Sum
- A Partial Sum of 1^3, －2^3, 3^3, －4^3, 5^3, －6^3, ......
- A Simple Recurrence Relation

#Sequences #NumberTheory #ArithmeticSequences

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At 2:39, (2a+n-1)-n must be 2a-1, not 2a+1. However, 2a-1>0 still holds when a is natural number.