Sn = (1+(1/n))^n (a) Prove Sn is strictly increasing (b) bounded below by 2 and above...

Sn = (1+(1/n))^n

(a) Prove Sn is strictly increasing (b) bounded below by 2 and above by 3

(c) Sn converges to e

(d) Obtain an expression for e

(e) Prove e is irrational

Expert Solution

Colby Messinger answered 1 year ago

Show that (a)Sn=<(1 2),(1 3),……(1 n)>. (b)Sn=<(1 2),(2 3),……(n-1 n)> (c)Sn=<(1 2),(1 2 …… n-1 n)>

Prove that if a sequence is bounded, then limsup sn is a real number.

Show that if S is bounded above and below, then there exists a number N >...

Show that if S is bounded above and below, then there exists a number N > 0 for which - N < or equal to x < or equal to N if x is in S

4. Prove that for any n∈Z+, An ≤Sn.

Prove that Sn is generated by {(i i + 1) I 1 < i < n - 1}.

Prove that if f is a bounded function on a bounded interval [a,b] and f is...

Prove that if f is a bounded function on a bounded interval [a,b] and f is continuous except at finitely many points in [a,b], then f is integrable on [a,b]. Hint: Use interval additivity, and an induction argument on the number of discontinuities.

(a) Prove that Sn is generated by the elements in the set {(i i+1) : 1≤i≤n}....

(a) Prove that Sn is generated by the elements in the set {(i i+1) : 1≤i≤n}. [Hint: Consider conjugates, for example (2 3) (1 2) (2 3)−1.] (b) ProvethatSn isgeneratedbythetwoelements(12)and(123...n) for n ≥ 3. (c) Prove that H = 〈(1 3), (1 2 3 4)〉 is a proper subgroup of S4.

Question

Sn = (1+(1/n))^n (a) Prove Sn is strictly increasing (b) bounded below by 2 and above...

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