4.1.7 - Mathematical Induction.sagews

s = 1
n = 5
for k in [2..n]:
    s = s + k^2
s
print '1^2 + 2^2 + ... + ', n^2 , '=', s

55 1^2 + 2^2 + ... + 25 = 55

n*(n+1)*(2*n+1)/6

55

f=x^2
n=5
print '1^2 + 2^2 + ... +', n^2, '=', sum(f,x,1,n)

1^2 + 2^2 + ... + 25 = 55