1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
S_A_V [24]
3 years ago
11

What’s the value of the expression?

Mathematics
2 answers:
WITCHER [35]3 years ago
8 0

Answer:

hi how are you

Step-by-step explanation:

Fofino [41]3 years ago
3 0

The answer to the expression is 42.

You might be interested in
Compute the sum:
Nady [450]
You could use perturbation method to calculate this sum. Let's start from:

S_n=\sum\limits_{k=0}^nk!\\\\\\\(1)\qquad\boxed{S_{n+1}=S_n+(n+1)!}

On the other hand, we have:

S_{n+1}=\sum\limits_{k=0}^{n+1}k!=0!+\sum\limits_{k=1}^{n+1}k!=1+\sum\limits_{k=1}^{n+1}k!=1+\sum\limits_{k=0}^{n}(k+1)!=\\\\\\=1+\sum\limits_{k=0}^{n}k!(k+1)=1+\sum\limits_{k=0}^{n}(k\cdot k!+k!)=1+\sum\limits_{k=0}^{n}k\cdot k!+\sum\limits_{k=0}^{n}k!\\\\\\(2)\qquad \boxed{S_{n+1}=1+\sum\limits_{k=0}^{n}k\cdot k!+S_n}

So from (1) and (2) we have:

\begin{cases}S_{n+1}=S_n+(n+1)!\\\\S_{n+1}=1+\sum\limits_{k=0}^{n}k\cdot k!+S_n\end{cases}\\\\\\
S_n+(n+1)!=1+\sum\limits_{k=0}^{n}k\cdot k!+S_n\\\\\\
(\star)\qquad\boxed{\sum\limits_{k=0}^{n}k\cdot k!=(n+1)!-1}

Now, let's try to calculate sum \sum\limits_{k=0}^{n}k\cdot k!, but this time we use perturbation method.

S_n=\sum\limits_{k=0}^nk\cdot k!\\\\\\
\boxed{S_{n+1}=S_n+(n+1)(n+1)!}\\\\\\


but:

S_{n+1}=\sum\limits_{k=0}^{n+1}k\cdot k!=0\cdot0!+\sum\limits_{k=1}^{n+1}k\cdot k!=0+\sum\limits_{k=0}^{n}(k+1)(k+1)!=\\\\\\=
\sum\limits_{k=0}^{n}(k+1)(k+1)k!=\sum\limits_{k=0}^{n}(k^2+2k+1)k!=\\\\\\=
\sum\limits_{k=0}^{n}\left[(k^2+1)k!+2k\cdot k!\right]=\sum\limits_{k=0}^{n}(k^2+1)k!+\sum\limits_{k=0}^n2k\cdot k!=\\\\\\=\sum\limits_{k=0}^{n}(k^2+1)k!+2\sum\limits_{k=0}^nk\cdot k!=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\\\\\\
\boxed{S_{n+1}=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n}

When we join both equation there will be:

\begin{cases}S_{n+1}=S_n+(n+1)(n+1)!\\\\S_{n+1}=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\end{cases}\\\\\\
S_n+(n+1)(n+1)!=\sum\limits_{k=0}^{n}(k^2+1)k!+2S_n\\\\\\\\
\sum\limits_{k=0}^{n}(k^2+1)k!=S_n-2S_n+(n+1)(n+1)!=(n+1)(n+1)!-S_n=\\\\\\=
(n+1)(n+1)!-\sum\limits_{k=0}^nk\cdot k!\stackrel{(\star)}{=}(n+1)(n+1)!-[(n+1)!-1]=\\\\\\=(n+1)(n+1)!-(n+1)!+1=(n+1)!\cdot[n+1-1]+1=\\\\\\=
n(n+1)!+1

So the answer is:

\boxed{\sum\limits_{k=0}^{n}(1+k^2)k!=n(n+1)!+1}

Sorry for my bad english, but i hope it won't be a big problem :)
8 0
3 years ago
Will mark brainliest on the best answer and also explain how you got that answer.
natulia [17]

Answer:

i think it's about 20 im not 100 percent sure :/

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
What's y / 4 equals -3​
katovenus [111]

Y/4 = -3

Multiply both sides by 4

Y = -12

8 0
3 years ago
Read 2 more answers
At what points are the equation y=x^2 and 1/x+2 equal<br><br>​
irina [24]

Answer:

Brown, purple, Green and Red/Pink

Step-by-step explanation:

The equations are equal where they intersect on the graph. There are 4 points at which the to graphs intersect. They intersect at the points colored brown, purple, green and red.

6 0
3 years ago
A (0,5)<br> B (3, 11)<br> What’s the equation
slava [35]
Y=2x+5
goes up by 2, which is the gradient and 5 is the y intercept
6 0
1 year ago
Other questions:
  • Can somebody help me
    7·1 answer
  • A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints
    14·1 answer
  • Find the median of the following set of data. Round to the nearest tenth if necessary. 26.1, 8.4, 11.4, 44.1, 32.3, 46, 41, 18.5
    11·2 answers
  • To which set of real numbers does the following number belong?
    12·2 answers
  • Graph each equation x/3 -y/6 = 1
    7·1 answer
  • 400000 to the nearest ten thousand
    6·1 answer
  • The miniature golf scores for 7 friends are 23, 30, 39, 32, 35, 14, and 23. What is the mean golf score for this group of friend
    11·1 answer
  • What is a statistical error?
    13·1 answer
  • 1/4x -5=3/4x-12 show two different ways to solve
    11·1 answer
  • $2.99 for 17 lb<br> What the answer
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!