3 years ago

What is thr probability of rolling a 5 on a six-sided number cube?

Mathematics

1 answer:

Afina-wow [57]3 years ago

6 0

Answer: 1/6

Step-by-step explanation:

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

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

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

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

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

ok I'm bout to get to the point my mother hates people that don't are not straight and I'm bi so how do I come out to my mom and

Vlada [557]

Answer:

you should life make a cake and put frosting words on it that say I'm bi and i'm proud!

3 0

3 years ago

Read 2 more answers

2 is underlined 12.917 what is the place value for 2

Nadya [2.5K]

Answer: 2 is the nearest whole number.