Series - Some finite series

Number of terms in the Series : n

1. 1+2+3+...+n =$n(n+1) \over 2$
2. 2+4+6+...+2n = $n(n+1)$
3. 1+3+5+...+(2n-1)=$n^2$
4. k+(k+1)+(k+2)+...+(k+n-1)=$n(2k+n-1) \over 2$
5. $1^2+2^2+3^2+...+n^2= {n(n+1)(2n+1) \over 6 }$
6. $1^3+2^3+3^3+...+n^3= \bigg[{n(n+1) \over 2} \bigg]^2$
7. $1^2+3^2+5^2+...+(2n-1)^2= {n(4n^2-1) \over 3 }$
8. $1^3+3^3+5^3+...+(2n-1)^3= n^2(2n^2-1 )$
9. $1+{1 \over 2}â€‹â€‹â€‹â€‹â€‹â€‹+â€‹â€‹{1 \over 4}+{1 \over 8}+...+{1 \over 2^n}+...=2$
10. ${1 \over 1.2 }+{1 \over 2.3 }+{1 \over 3.4 }+...+{1 \over n(n+1) }+...=1$
11. $1+{1 \over 1! }+{1 \over 2! }+{1 \over 3! }+...+{1 \over (n-1)! }+...=e$