Ask question

Ask question

All categories

2 years ago

9

In mathematics, the Nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/N. So, the first harmonic number is 1, th

e second is 1.5, the third is 1.83333... and so on. Assume that n is an integer variable whose value is some positive integer N. Assume also that cl is a variable whose value is the Nth harmonic number. Write an expression whose value is the (N+1)th harmonic number.

1 answer:

Andreyy892 years ago

3 0

Answer:

cl + 1/(N+1)

Step-by-step explanation:

If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl

And we know that the (N+1)th harmonic number can be found by doing

1+1/2+1/3+1/4+...+1/N+1/(N+1)

=cl + 1/(N+1)

The (N+1)th harmonic number is cl + 1/(N+1) given that the Nth term is cl

Other way to see the answers:

Maybe you want to write it as a single fraction so you have

[cl(N+1)+1]/(N+1)=[cl*N+cl+1]/(N+1)

You might be interested in

The number of calls coming per minute into a hotel reservation center is Poisson random variable with mean 3.

natima [27]

Answer:

a) 0.05

b) 0.9826

c) 0.000039308

Step-by-step explanation:

a) $P_X(0) = \frac{e^{-3}3^0}{0!} = e^{-3} = 0.05$

b) For two minutes, the mean is doubled, hence it is 6. In order to calculate the probability of al least two calls arriving, we calculate first the probability of the complementary event: At most 1 call will arrive. For that probability, we need to sum the probabilities of 0 and 1.

$P_X(0) = e^{-6}$

$P_X(1) = \frac{e^{-6}*6^1}{1!} = 6*e^{-6}$

Hence,

$P(X \geq 2) = 1-P(X < 2) = 1- 7*e^{-6} = 0.9826$

c) For five minutes the mean is 15. We need to sum the probabilities of 0, 1 and 2.

$P_X(0) = e^{-15}$

$P_X(1) = e^{15}*15$

$P_X(2) = \frac{e^{-15}*15^2}{2!} = 112.5*e^{-15}$

As a result,

$P(X \leq 2) = e^{-15}(1+15+112.5) = 0.000039308$

Practically 0

4 0

2 years ago

21. Given directed line segment WV , find the coordinates of R

Jobisdone [24]

Answer:

$R\left(\frac {4x_1+3x_2}{7} , \frac {4y_1+3y_2}{7}\right)$

Step-by-step explanation:

Let the coordinate of the points W, V and R are $(x_1,y_1), (x_2,y_2),$ and $(x_s,y_s)$ respectively.

The coordinate of the section point, $(x_s,y_s),$ which divides the line joining the two points $(x_1,y_1)$ and $(x_2,y_2)$ in the ration $m:n$ is

$x_s=\frac {nx_1+mx_2}{m+n}$ and

$y_s=\frac {ny_1+my_2}{m+n}$ .

The given ration is, $m:n=3:4$

$R(x_s,y_s)=R\left(\frac {nx_1+mx_2}{m+n} , \frac {ny_1+my_2}{m+n}\right)$

$=R\left(\frac {4x_1+3x_2}{7} , \frac {4y_1+3y_2}{7}\right)$ .

The exact point can be determined by putting the value of the exact coordinate in the above-obtained formula.

6 0

2 years ago

What is the equation of the line? Iready

leva [86]

Answer:

C

Step-by-step explanation:

The y intercept is 2 and if you do the rise/run you'll find that the slope has to be 1/2

this means our equation has to be

1/2x+2

7 0

1 year ago

Read 2 more answers

Marks age, X is six times his age 2 years ago. which equation represents the statement

FinnZ [79.3K]

x=6x-2 This would be your answer, hope this helps if you need any further explanation feel free to let me know and I would be happy to help you out.

6 0

2 years ago

Read 2 more answers

John painted his most famous work,in his country,in 1930 on composition board with perimeter 103.48 in. If the rectangular paint

Alexxandr [17]

Answer:

Width $=22.955$ in

length $=28.785$ in

Step-by-step explanation:

let width $=x$

painting is $5.83$ in taller than it is wide

length $=x+5.83$

Perimeter of rectangle $=2$ (length+width)

Perimeter of painting $=103.48$

$2(x+x+5.83)=103.48\\2x+5.83=51.74\\2x+51.74-5.83\\2x=45.91\\x=\frac{45}{2} \\x=22.955$

width $=x=22.955$ in

length $=x+5.83=22.955+5.83=28.785$ n

5 0

2 years ago