Real Analysis Answers

Prove if |x_sub(n) - L| <= b_sub(n) and lim b_sub(n)=0, then lim x_sub(n)=L

Using the binomial theorem, find the limit of Sn=(1+1/n)^n-1

Task
If (a sub_n) and (b sub_n) are cauchy sequences, show directly that (a sub_n * b sub_n) is also a cauchy sequence.
Detailed explanation: NO
Specific requirements:
Prove

Prove: A subset S of the real numbers is closed if and only if lim (as n goes to infinity) X_n is an element of S whenever (X_n) is a convergent sequence whose terms are all in S.

what are dummy variables?

Dear Expert sir i have anohter question.give me an example of a sequence which is both geometric as well as arithmetic.a lot of thanks .

Show that a set can't be a neighborhood of its supremum.

A cafeteria offers a complete dinner that includes one serving each of appetizer, soup, entrée, and dessert for $6.99. If the menu has four appetizers, four soups, seven entrées, and two desserts, how many different meals are possible?

Let xn is greater than or equal to 0 for all n belongs to N.
(a) If xn converges to 0, show that sqrt (xn) converges to 0.
(b) If xn converges to x, show that sqrt (xn) converges to xn.

Let f be a function from A into X, and let Y, Z be proper subsets of X. How do I prove
the inverse function of X = A and
the inverse function of (Y') = the inverse function of (Y)"