All categories

4 years ago

Find the sum of the infinite series 1/3+4/9+16/27+64/81+.... if it exists.

1 answer:

6 0

9/27, 12/27, 16/27

So this is a geometric sequence as each term is 4/3 the previous term.

Since the common ration is greater than one the sum of the series diverges, it does not exist. (The sum just keeps getting larger and larger)

For a geometric series to have a sum r^2<1

So that the normal sum....

s(n)=a(1-r^n)/(1-r) becomes if r^2<1

s=a/(1-r)

You might be interested in

Blake gives piano lessons in the evenings.

Aliun [14]

Answer:

The correct answer is B. {0, 20, 40, 60, 80, 100, 120}

Step-by-step explanation:

1. Let's check all the information given to answer this question correctly:

Rate of each piano lesson Blake gives = US$ 20

Blake can give between 0 and 6 lessons every evening

Earnings = Number of lessons * Rate of each lesson

2. What is the range of this relation?

Let's recall that the domain of a relation is the set of all values for which the relation is defined, and the range of the relation is the set of all values that the relation takes.

It means that the domain of the relation in this case is the number of lessons that Blake can give every evening:

{0, 1, 2, 3, 4, 5, 6}

And the range of this relation is the amount Blake earns in an evening depending on the number of lessons he gives:

{0, 20, 40, 60, 80, 100, 120}

The correct answer is B. {0, 20, 40, 60, 80, 100, 120}

3 0

3 years ago

Read 2 more answers

What is 2 and 5/6 divided by 6 and 4/5

9966 [12]

Firstly I would revert these back to improper fractions:

So 17/6 ÷ 24/5

Then I would use keep, change, flip

So 17/6 * 5/24

Finally simplify

85/144

Final Answer: 85/144

3 0

3 years ago

If a train traveled at 50 meters within 120 seconds, what is its speed?

Alja [10]

Answer:

v = 0.416 m/s

Step-by-step explanation:

Give that,

Distance covered by a train, d = 50 m

Time taken, t = 120 s

We need to find the speed of a train. The formula for speed of an object is equal to the total distance covered divided by total time taken. It can be given by :

$v=\dfrac{d}{t}\\\\v=\dfrac{50\ m}{120\ s}\\\\v=0.416\ m/s$

So, the speed of a train is 0.416 m/s.

3 0

3 years ago

A coin is tossed 13 times how many different outcomes are possible

makvit [3.9K]

Since the toss can either be heads or tails and only one of these can land at a time the answer is 13

5 0

3 years ago

Read 2 more answers

Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.

Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function f(x, y) for which

grad f(x, y) = F(x, y)

This amounts to solving for f such that

∂f/dx = x + 3

∂f/∂y = 6y + 3

Integrating both sides of the first equation with respect to x gives

f = 1/2 x ^2 + 3x + g(y)

Differentiating with respect to y gives

∂f/∂y = dg/dy = 6y + 3

Solving for g gives

g = ∫ (6y + 3) dy = 3y ^2 + 3y + C

and hence

f(x, y) = 1/2 x ^2 + 3x + 3y ^2 + 3y + C

(a) By the fundamental theorem, the integral of F along any path starting at the point P (1, 0) and ending at Q (3, 3) is

∫ F(x, y) • dr = f (3, 3) - f (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to P :

∫ F(x, y) • dr = f (1, 0) - f (0, 0) = 7/2 - 0 = 7/2

• From Q back to the origin:

∫ F(x, y) • dr = f (0, 0) - f (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

6 0

3 years ago