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RUDIKE [14]
2 years ago
13

!!!KHAN ACADEMY!!! help please

Mathematics
1 answer:
barxatty [35]2 years ago
3 0
Use photomath lollllll
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Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...
Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the <em>n</em>th term in the sequence is multiplied by <em>n</em>/(<em>n</em> + 1) to get the (<em>n</em> + 1)th term.

Recursively, the sequence is given by

\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}

We can solve this exactly by iterating:

a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots

and so on down to

a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1

or

a_n=\dfrac{(n-1)!}{n!}a_1

and with lots of cancellation, we end up with

a_n=\dfrac{a_1}n=\boxed{\dfrac2n}

6 0
2 years ago
The sum of three consecutive integers is 168. What are the integers
sesenic [268]

Answer:

55,56,57

Step-by-step explanation:

4 0
1 year ago
A telephone company in germany charges 0.12 euro per minute to call the US after a connection fee of 1.50 euro what is the total
Nana76 [90]

Answer:

Total minutes = 47 Minutes

Step-by-step explanation:

A telephone company in germany charges 0.12 euro per minute to call the US after a connection fee of 1.50 euro

Expressing the statement in mathematical terms;

Cost = 0.12x + 1.5 where x represens minutes

if the cost of the call was 7.14 euro, total minutes  = ?

7.14 = 0.12x + 1.5

7.14 - 1.5 = 0.12x

5.64 = 0.12x

x = 5.64 / 0.12 = 47

Total minutes = 47 Minutes

8 0
3 years ago
Can somebody plz answer all of them correct! (Only if u done this before)
swat32

Answer:

23) 53/100

24)2/5

25)3/5

26)11/50

27)17/50

28)19/1000

29)4/5

30)1/250

31)9/25

32)1 3/10

33)11 1/2

34) 7 3/40

Step-by-step explanation: Hope this helps!

7 0
2 years ago
Find the mean of the following data set. 8, 5, 15, 12, 10 12.5 10 14 50
cluponka [151]

Answer:

10

Step-by-step explanation:

8+5+15+12+10= 50 / 5 = 10

7 0
3 years ago
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