4.1.10 Mathematical Induction (Factorial).sagews

factorial(3)

6

for n in [0..10]:
    n,factorial(n)

(0, 1) (1, 1) (2, 2) (3, 6) (4, 24) (5, 120) (6, 720) (7, 5040) (8, 40320) (9, 362880) (10, 3628800)

for n in [0..10]:
    n,factorial(n),2^n

(0, 1, 1) (1, 1, 2) (2, 2, 4) (3, 6, 8) (4, 24, 16) (5, 120, 32) (6, 720, 64) (7, 5040, 128) (8, 40320, 256) (9, 362880, 512) (10, 3628800, 1024)

for n in [0..15]:
    n,factorial(n),5^n

(0, 1, 1) (1, 1, 5) (2, 2, 25) (3, 6, 125) (4, 24, 625) (5, 120, 3125) (6, 720, 15625) (7, 5040, 78125) (8, 40320, 390625) (9, 362880, 1953125) (10, 3628800, 9765625) (11, 39916800, 48828125) (12, 479001600, 244140625) (13, 6227020800, 1220703125) (14, 87178291200, 6103515625) (15, 1307674368000, 30517578125)