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3 years ago

What is 1.05 as an improper fraction

Mathematics

1 answer:

lozanna [386]3 years ago

5 0

21/20 ,because 0.5 is 1/20 of the whole number 1,so 20/20 + 1/20=21/20

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

3 years ago

Y=-3x + 7? what is slope of line y

ipn [44]

Answer:

-3

Step-by-step explanation:

coefficent of x enough to understand slope

4 0

3 years ago

I need help please ????

Rudiy27

9514 1404 393

Answer:

see attached

Step-by-step explanation:

I like to use a spreadsheet for repetitive calculations. The distances are computed from the distance formula:

d = √((x2 -x1)^2 +(y2 -y1)^2)

The results are shown in the second attachment. The drawing in the first attachment has the lengths rounded to the nearest tenth.

7 0

3 years ago

The data represents the height, in feet, of various buildings. Find the Interquartile Range.

N76 [4]

Answer: 6

Step-by-step explanation:

7 0

3 years ago

Can someone help me with this plz??

Anarel [89]

Answer:

f(-3) = -2(-3)^3 - 3

f(-3) = 54 - 3

f(-3) = 51

g(3) = -5(3) + 4

g(3) = -15+4

g(3) = -11

Hope this helps!

5 0

3 years ago