### Converging sequence

I would like help on the following problem: Suppose {a_n} is a sequence that satisfies the condition lim n-> oo (a_n+1 - a_n)=0. Prove that the sequence {a_n / n} converges to 0.

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I would like help on the following problem: Suppose {a_n} is a sequence that satisfies the condition lim n-> oo (a_n+1 - a_n)=0. Prove that the sequence {a_n / n} converges to 0.

The problem is Take any of the generalizations about the Fibonacci Numbers that we have considered, and investigate what happens if the sequence is formed by two different starting numbers but continues in the same way by adding successive pairs of terms. For example, you might form a new pseudo-Fibonacci sequence in this w

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Solve the first order homogeneous equation : x^2+y^2-2xyy'=0

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Joe has to take a test which consists of short-answer questions worth 9 points each and essay questions worth 25 points each. He must do at least 9 short-answer questions, but won't have time to do more than 10. He has to answer at least 3 essay questions, but can't spend time to do more than 10. If no more than 19 questions can

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Sally runs 2 mph faster than Paul throughout a 10 mile race. If Sally finishes 25 minutes ahead of Paul, what was Sally's time for the race?

Page 371 & 372 Solve each proportion # 28. 9 3 --- = --- X 2 # 31. 5 3 --- = ---- 9 x # 39. a a + 3 ------ = -------- A + 1 a # 41. m - 1 m - 3 ----------- = ---------

Completing the square problems: HYPERBOLAS- Find the center, vertices, foci, and asymptotes of the hyperbola. Please give the equation in standard form, i.e. (x-h)^2/a^2 - (y-k)^2/b^2=1 or other way around. 15) ? 9x^2-y^2-36x-6y+18=0 Answer: Center (2,-3) Vertices (3,-3), (1,-3) Foci: (2+ or √10, -3)

1st one: A family has a rectangular kitchen which measures 12 by 18 feet. They want to put diagonal heating coils in the floor of the room. How much will it cost them to put in the coils if they cost $25 foot? 12 x18 =216= Area 216x25= 5400 but since they want to put diagonals would I take half of this? 2nd one: A wi

1st one- One leg of an isosceles right triangle measures 12 meters long. Find the length of the hypotenuse of the triangle.? Would it be 12 over the sq rt of 2 2nd one A wire is needed to support a vertical pole 18ft tall. A cable will be anchored to a stake and it forms a 30 degree with the ground. nearest tenth... How fa

The 42 kilometer drive from Oakdale to Ridgemont usually takes 28 minutes. Because highway construction requires reduced speed limit, the trip now takes 14 minutes longer. Find the reduced speed limit in km/hr.

An explanation of the steps to use in a problem involving square roots in a system of equations using the sample problem given. Thank You. Please see attached.

I am having a problem trying to understand the given sample of a system of equations that has logarithms.

What are the inflection points? (a) f(x) = 12x^5 +15x^4 -240x^3+19 (One of the inflections is 0. Find the rest. Results cannot be -2.82 and 2.07) (b) f(x) = (x^2 - 8x + 32)(x-4)

Find the LCD for the given rational expression, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. Page 345 # 47. x y 1 ----, ------, ------ 9y^5 12x^3 6x^2y # 48 5 3b 1 -------, -------,

Find two positive numbers that satisfy the given requirements The product is 192 and the sum is a minimum

(1-3v) s=1.59t solve for V

A boat is being pulled into a dock with a rope attached to the boat at water level. when the boat is 12 feet from the dock, the length of the rope from the boat to the dock is 3 feet longer than twice the height of the dock above the water. - Determine the equation needed to find the height of the dock. - Find the height

An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/second. It's distance, s(t) in feet above the ground after t seconds is given by the equation: s(t)=-16^2+144t+100 - find the maximum height, s(t), of the object above the ground. - find the height of the building, th

THE DEPTH OF CUT OFF {d} FOR A SHEET PILED RETAINING WALL IS GIVEN BY ONE OF THE SOLUTIONS OF THE FOLLOWING EQUATION; 27.402d3+223.518d2=364.7 FIND THE REQUIRED VALUE OF d TO THE NEAREST 0.1 METRE

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K. Let S be the subspace of F. Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

There are 176 passengers going from Boston to Denver on an Amtrak. The regular coach seat are $103 and sleeper coach seat are $199 . The receipt total was 24,080.00 . How do I find out many passenger purchase what type of ticket?

Need help learn all the steps to solve these problems. See the attached file.

1. A sphere of radius 1 is totally submerged in a cylindrical tank of radius 4 as shown. The water level in the tank rises a distance of h. What is the value of h? 2. A cube has a surface area of 6x. What is the volume? 3. A sphere has a radius of r. If this radius is increased by b, then the sphere's surface area is increased

M*(A) = inf ( A subset of M) of the sum of |M_i|. If A is a subset of K_s, where K_s = { -s =< x_i =< s} Then show that M*(A) = S^n - M*(A^c) A^c is compliment of A ( I think compliment of A in K_s ? )

Give a example of countable subset l^2 ( it is the class of all sequences which are bounded ) which is dense in l^2 ?