以下等式或者不等式均可以用数学归纳法予以证明！
1 + 3 + 5 + ... + (2n - 1) = n^2
1*2 + 2*3 + 3*4 + ... + n*(n + 1) = n*(n + 1)*(n + 2) / 3
1*1! + 2*2! + 3*3! + ... + n*n! = (n + 1)! - 1
1^2 + 2^2 + 3^2 + ... + n^2 = n*(n + 1)*(2n + 1) / 6
1^2 - 2^2 + 3^2 -... + (-1)^n * n^2 = (-1)^(n + 1) * n * (n + 1) / 2
2^2 + 4^2 + ... + (2n)^2 = 2n*(n+1)*(2n+1) / 3
1/2! + 2/3! + ... + n/(n+1)! = 1 - 1/(n+1)!
2^(n
