3 years ago

Needs to be checked.............

Mathematics

2 answers:

Lubov Fominskaja [6]3 years ago

7 0

B. is the correct answer you got it right

Malory your fellow helper

blondinia [14]3 years ago

7 0

That should be right

You might be interested in

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

$\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

4 0

3 years ago

I really really need this answer PLSSSSSSSSS

ikadub [295]

Answer: x=112

Step-by-step explanation: If you add 35 and 33 you would get 68 and if you subtract 68 from 180 you will get 112. I hope this helps!

5 0

3 years ago

Read 2 more answers

Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80.

Anvisha [2.4K]

Answer: $9.00

.......................................

4 0

3 years ago

What are the solutions of the quadratic equation (x + 3)2 = 49

Korvikt [17]

the right answer is

x = 4 and x = –10

I just take the test and I got it right I hope yall get it right to

8 0

3 years ago

Read 2 more answers

When lines are at the same distance apart over their lengths they are ?

svlad2 [7]

Answer:

parallel lines

Step-by-step explanation:

parallel lines are lines that do not meet each other

7 0

3 years ago