(a) Prove that n!/k!(n − k)! is always an integer. (b) For your computer, for what value of n will XXXXXXXXXXlead to an overflow? Compare the evaluation of e−x for x = 1, 2, 3, 4 using: (a) the...

(a) Prove that n!/k!(n − k)! is always an integer. (b) For your computer, for what value of n will (2.3.2) lead to an overflow?

Compare the evaluation of e−x for x = 1, 2, 3, 4 using: (a) the alternating series e−x = 1 − x + x2 /2 − x3 /3! +···+ (−1)j xj /j! +··· ; (b) the reciprocal of the nonalternating series

                                         1/(1 + x + x2 /2 + x3 /3! +···+ xj /j! +···).