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2 years ago

CaN YOu HeLP Me PleAse????????

Mathematics

1 answer:

Orlov [11]2 years ago

4 0

Answer:

Triangle Exterior Angle Theorem

Step-by-step explanation:

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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

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2 years ago

Are multiples of 3 are always multiples of 6? True or False.

MissTica

Answer:

False

Step-by-step explanation:

9 is a multiple of 3 but not 6

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(9x +1) 45 = (x+5) 14

ipn [44]

Use the website math papa it’ll give you the answers for your problem I promise!! Have a good day :)

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2 years ago

How do find a number out of a percent

Nana76 [90]

You only have the % and you need the number. For example i got a 87% on my Math test what is that as a decimal? The answer is 0.87 because you move the decimal ahead 2 numbers.

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3 years ago

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(8, -3), m = 2 point slope form equation

pentagon [3]

Answer:

y=2x+14

Step-by-step explanation:

y=mx+b

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2 years ago

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