1+2+3+4+5+.............+1000000000000000000 Is ≈50000000005000000000 and ITS wrong because i use "≈" ITS just eee, sugesting
Analysis
The claim concerns the approximate sum of all integers from 1 up to 1,000,000,000,000,000,000 (one quintillion), estimated as roughly 50,000,000,005,000,000,000. This aligns with the well-known arithmetic series formula for the sum of the first n natural numbers: n(n+1)/2. Although the sources provided focus on smaller ranges (mostly up to 100 or 1,000), they consistently confirm the validity of this formula. The claim’s use of "≈" (approximately) is appropriate given the extremely large number, but mathematically the exact sum is n(n+1)/2, which for n = 10^18 yields exactly 500,000,000,0500,000,000,000. The claim’s approximate figure is slightly off by a factor of 10, but the principle and method are correct. The sources, while not from highly authoritative academic references, consistently support the arithmetic progression summation formula, which is a fundamental and proven mathematical fact.
Sources
Explains the pairing technique for sums up to 100 but does not address extremely large numbers.
Discusses methods for summing numbers up to 100, supporting the arithmetic series formula.
Uses geometric interpretation for sums up to 10, indirectly supporting the formula.
Provides programming approach for summing 1 to 100, confirming the summation concept.
Explicitly states Gauss’s formula for sum of 1 to 100, foundational for the claim.
Focuses on a modified sum excluding digits, irrelevant to the claim.
Clearly states the formula n(n+1)/2 for sums up to 100, directly supporting the claim’s basis.
Discusses sums of powers, not directly the linear sum, but related.
Applies formula to sum up to 1,000, consistent with the claim’s method.
Describes Gauss’s pairing method, foundational to the claim’s correctness.
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