Question #1

Prove that limit as n --> infinity of

(1 + 1/n)**n = e = 1 +1/1! + 1/2! + 1/3! + 1/4! + . . .

By binomial theorem,

(1+ 1/n)**n

= 1 + n * (1/n) + (n(n-1)/2) * (1/n)**2

+ (n(n-1)(n-2)/3!) * (1/n)**3 + . . .

Take the limit as n--> infinity.

limit as n --> infinity of (1 + 1/n)**n

is 1 + 1 + 1/2 + 1/3! + . . . = e.

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