All categories

3 years ago

Does this sum converge: show steps

Mathematics

1 answer:

ehidna [41]3 years ago

6 0

Answer:

Yes

Step-by-step explanation:

$\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }$

If we say u = √n, then:

$\sum_{u=1}^{\infty} (\frac{1}{e})^{u}$

This is a geometric series. Since |1/e| < 1, the series converges.

You might be interested in

Isamasonip invested $2.000 in

alexgriva [62]

Answer:

Compound Interest= $3440

Final Amount= $5440

Step-by-step explanation:

Compound Interest's formula= P(1+r/100)^n

where P is Principal, r is Rate then n is Years

So in this case,,2000(1+.72)^1 = $3440

Hence, Total Amount = Principal+Interest

therefore T.A= $2000+$3440

T.A=$5440

Thanks... Subjected to Review

7 0

2 years ago

A triangle has legs that are 7in and 24in long. How long is the hypothenuse?

SashulF [63]

Answer: 25 in

Step-by-step explanation:

<u>Due to the use of the term "hypotenuse" I will assume the triangle is a right triangle.</u>

<u></u>

According to pythagorean theorem, 7²+24²=(hypotenuse)²

49+24²= (hypotenuse)²

49+576= (hypotenuse)²

625 = (hypotenuse)²

25 = hypotenuse

Hope it helps <3 :D

6 0

2 years ago

At a baseball game, a vender sold a combined total of 170 sodas and hot dogs. the number of hot dogs sold was 50 less than the n

Juliette [100K]

Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.

x+y=170 (We know that soda + dogs is 170)

x-50=y (We know that dogs is equal to 50 less than sodas)

We can use substitution to solve this system of equations.

x+y=170

Sub in the value of y from the second equation

x+(x-50)=170

2x-50=170

2x=220

x=110

We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.

x+y=170

110+y=170

y=60

So, there were 60 hotdogs sold and 110 sodas sold.

8 0

3 years ago

What is (4x+-7)(2x+-9)

uysha [10]

Answer:x=1

Step-by-step explanation:(4x+-7)=(2x+-9)

We move all terms to the left:

(4x+-7)-((2x+-9))=0

We add all the numbers together, and all the variables

(4x-7)-((2x-9))=0

We get rid of parentheses

4x-((2x-9))-7=0

We calculate terms in parentheses: -((2x-9)), so:

(2x-9)

We get rid of parentheses

2x-9

Back to the equation:

-(2x-9)

We get rid of parentheses

4x-2x+9-7=0

We add all the numbers together, and all the variables

2x+2=0

We move all terms containing x to the left, all other terms to the right

2x=-2

x=-2/2

x=-1

(4x+-7)=(2x+-9)

We move all terms to the left:

(4x+-7)-((2x+-9))=0

We add all the numbers together, and all the variables

(4x-7)-((2x-9))=0

We get rid of parentheses

4x-((2x-9))-7=0

We calculate terms in parentheses: -((2x-9)), so:

(2x-9)

We get rid of parentheses

2x-9

Back to the equation:

-(2x-9)

We get rid of parentheses

4x-2x+9-7=0

We add all the numbers together, and all the variables

2x+2=0

We move all terms containing x to the left, all other terms to the right

2x=-2

x=-2/2

x=-1

8 0

2 years ago

For what value of h is 24=(h/10)-6

kondor19780726 [428]

Answer:

$h=300$

Step-by-step explanation:

we have

$24=(\frac{h}{10})-6$

Solve for h

That means----> Isolate the variable h

Adds 6 both sides

$24+6=(\frac{h}{10})-6+6$

$30=\frac{h}{10}$

Multiply by 10 both sides

$30*10=\frac{h}{10}*(10)$

$h=300$

6 0

2 years ago