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1.
Sum of the first n numbers
1+2+3+⋯+n=n(n+1)21+2+3+ \cdots + n = \dfrac{n(n+1)}{2}
Finite sum
2.
Sum of the first n even numbers
2+4+6+⋯+2n=n(n+1)2+4+6+ \cdots + 2n = n(n+1)
Finite sum
3.
Sum of the first n odd numbers
1+3+5+…+(2n−1)=n21+3+5+\ldots+(2n-1) = n^2
Finite sum
4.
k+(k+1)+…+(k+n−1)=n(2k+n−1)2k + (k+1) + \ldots + (k+n-1) = \dfrac{n(2k+n-1)}{2}
Finite sum
5.
Sum of first n squares
12+22+32+…+n2=n(n+1)(2n+1)61^2+2^2+3^2+ \ldots + n^2 = \dfrac{n(n+1)(2n+1)}{6}
Finite sum
6.
Sum of first n cubes
13+23+33+…+n3=(n(n+1)2)21^3+2^3+3^3+ \ldots + n^3 = \left(\dfrac{n(n+1)}{2}\right)^2
Finite sum
7.
Sum of first n odd squares
12+32+52+…+(2n−1)2=n(4n2−1)31^2 + 3^2 + 5^2 + \ldots + (2n-1)^2 = \dfrac{n(4n^2-1)}{3}
Finite sum
8.
Sum of first n odd cubes
13+33+53+…+(2n−1)3=n2(2n2−1)1^3+3^3+5^3+ \ldots + (2n-1)^3 = n^2(2n^2-1)
Finite sum

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