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2. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

   en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

   Download as PDF; Printable version; ... The nth partial sum is given by a simple formula: ... Sum of Natural Numbers ...

3. Summation - Wikipedia

   en.wikipedia.org/wiki/Summation

   In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.

4. Proofs involving the addition of natural numbers - Wikipedia

   en.wikipedia.org/wiki/Proofs_involving_the...

   We prove associativity by first fixing natural numbers a and b and applying induction on the natural number c. For the base case c = 0, (a + b) + 0 = a + b = a + (b + 0) Each equation follows by definition [A1]; the first with a + b, the second with b. Now, for the induction. We assume the induction hypothesis, namely we assume that for some ...

5. Ibn al-Haytham - Wikipedia

   en.wikipedia.org/wiki/Ibn_al-Haytham

   Download as PDF; Printable version; In other projects ... He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the ...

6. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   1. Denotes addition and is read as plus; for example, 3 + 2. 2. Denotes that a number is positive and is read as plus. Redundant, but sometimes used for emphasizing that a number is positive, specially when other numbers in the context are or may be negative; for example, +2. 3.

7. Natural number - Wikipedia

   en.wikipedia.org/wiki/Natural_number

   The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0 ) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω .

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9. Ramanujan's sum - Wikipedia

   en.wikipedia.org/wiki/Ramanujan's_sum

   In number theory, Ramanujan's sum, usually denoted c q (n), is a function of two positive integer variables q and n defined by the formula c q ( n ) = ∑ 1 ≤ a ≤ q ( a , q ) = 1 e 2 π i a q n , {\displaystyle c_{q}(n)=\sum _{1\leq a\leq q \atop (a,q)=1}e^{2\pi i{\tfrac {a}{q}}n},}