Math Formulas Search

1.

Sum of the first n numbers

$1+2+3+ \cdots + n = \dfrac{n(n+1)}{2}$

2.

Sum of the first n even numbers

$2+4+6+ \cdots + 2n = n(n+1)$

3.

Sum of the first n odd numbers

$1+3+5+\ldots+(2n-1) = n^2$

4.

$k + (k+1) + \ldots + (k+n-1) = \dfrac{n(2k+n-1)}{2}$

5.

Sum of first n squares

$1^2+2^2+3^2+ \ldots + n^2 = \dfrac{n(n+1)(2n+1)}{6}$

6.

Sum of first n cubes

$1^3+2^3+3^3+ \ldots + n^3 = \left(\dfrac{n(n+1)}{2}\right)^2$

7.

Sum of first n odd squares

$1^2 + 3^2 + 5^2 + \ldots + (2n-1)^2 = \dfrac{n(4n^2-1)}{3}$

8.

Sum of first n odd cubes

$1^3+3^3+5^3+ \ldots + (2n-1)^3 = n^2(2n^2-1)$

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