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3 years ago

Sequences and Series precalc multiple choice, will give brainliest.

Mathematics

1 answer:

Gala2k [10]3 years ago

8 0

9514 1404 393

Answer:

False

Step-by-step explanation:

The given formula is the "explicit" formula for the sequence.

The recursive formula would be ...

a[1] = 160

a[n] = 1/2·a[n-1] . . . . each term expressed in as a function of previous terms

The given statement is false.

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Maslowich

Answer:

add the numbers and divide by how many numbers there are, thats how you find the mean

Step-by-step explanation:

3 0

3 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

The sum of 5 and the twice a number is at most 27

melamori03 [73]

Answer:

Step-by-step explanation:

let the number=x

5+2x≤27

2x≤25-5

2x≤20

x≤4

6 0

3 years ago

2,9,23,51,107 Determine the next terms of sequence

Ray Of Light [21]

Answer:

answer is 142

Step-by-step explanation:

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3 years ago

2( 5 1 m− 5 2 )+ 5 3

Fantom [35]

Answer:

uh I need the question...

Step-by-step explanation:

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3 years ago