Question: Show that sup{1 - 1/n : n N} = 1.

Show that sup{1 - 1/n : n ∈ N} = 1.

Step by Step Solution

★★★★★

3.35 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since 11n 1 for all n N the number ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

829-C-I (954).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Show that (9) in Sec. 12.6 with coefficients (10) is a solution of the heat equation for t > 0 assuming that f(x) is continuous on the interval 0 ¤ x ¤ L and has one-sided derivatives...

Q:

Consider the measurable space (W, A) and let A n A, n = 1, 2, then recall that And (i) Show that A n A n . (If also A n A n so that A n = n A n then this set is denoted by A n and is called the...

Q:

According to the WLLN (Application 1 to Theorem 9), if the r.v.s X 1 ,...,X n are i.i.d. with finite X 1 , then The following example shows that it is possible for {S n /n} to converge in probability...

Q:

Suppose that n people have their hats returned at random. Let Xi = 1 if the ith person gets his or her own hat back and 0 otherwise. Let Sn = n i=1 Xi. Then Sn is the total number of people who get...

Q:

=+5.48. Suppose that X1, X2,... are independent Exponential(1) random variables. According to Example 5.16, we have E(Xk i ) = k!, k = 1, 2,.... (i) Given k 2, define Yi = (Xi, Xk i ) . Show that...

Q:

cal 2 homework help Bb Revie Bb My GI & UTF-E VA MACZ VA 9. X Aska W Char G what f Login PB 5.1 P * Elasti G If the * HW4 Class Aller S How + X C A...

Q:

3. Let (S1) represent the series n + 5 n! n=in3 + n +3 and ($2) represent the series M n=inn Which one of the assertions below is true ? (A) Both series are convergent. (B) Both series are divergent....

Q:

2. *Prove 12+22+3 + + n = 1/n (n + 1)(2n + 1) for all natural numbers n N 3. Prove 7"-6n-1 is divisible by 36 for every n N.

Q:

Question 4: Consider a non-regular unary language, = { 1 } show that L = { 1^n | n is a prime number } is non-regular.

Q:

Problem 3.32 The random variable X has the discrete uniform distribution (see Equation 3.16). Show that V (X) = (N 1)(N + 1) 12 . Hint: Use the shortcut formula and Equation 3.15 for the moments of...

Q:

A bridge has mass 8000 kg. if a 3200 kg truck stops in the middle of the bridge what mass must each pier support

Q:

The Tire Division of Trakker Company produces tires for off-road sport vehicles. One-third of Tire's output is sold to an internal division of Trakker; the remainder is sold to outside customers....

Q:

E 1 8 - 6 identify temporary and permanent differences

Q:

Consider new product adopter categories and answer the following questions. a. Do you believe that consumers are always in the same category? For example, once a laggard, always a laggard? Can...

Q:

Evaluate the integral. a. x4/(x - 1) dx b. (5x + 1)/((2x + 1)(x - 1)) dx

Q:

Suppose that F, G, and Q are polynomials and F(x)/Q(x) = G(x)/Q(x) for all except when Q(x) = 0. Prove that F(x) = G(x) for all x.

Q:

If a 0 and is a positive integer, find the partial fraction decomposition of f(x) = 1/xn(x-a) First find the coefficient of 1/(x-a). Then subtract the resulting term and simplify what is left

Q:

A company retired $70 million of its 10% bonds at 102 ( $71.4 million) before their scheduled maturity. At the time, the bonds had a remaining discount of $2 million.\ Prepare the journal entry to...

Q:

Troy Engines, Ltd., manufactures a variety of engines for use in heavy equipment. The company has always produced all of the necessary parts for its engines, including all of the carburetors. An...

Q:

1. ((a) Progressive Services, Inc. has just declared a 7 for 3 stock split. The company's pre-split common stockholders' equity was as follows: If the pre-split price of common stock was $40, what...