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3 years ago

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Mathematics

2 answers:

mart [117]3 years ago

8 0

Answer:

On the second line, Alice didnt carry the negative in (-8). And for the 3rd line, she did 24 times 1/3, not 24 divided by 1/3.

Step-by-step explanation:

The correct answer would be, -360.

12*(0.25)*(-8)/(1/3)*5

3*(-8)/(1/3)*5

-24/(1/3)*5

-72*5

-360

I hope this is right!

Masja [62]3 years ago

7 0

Yeah yeah Nd then yeah

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You can try to show this by induction:

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

and

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

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From the given recurrence, we know

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

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

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

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

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

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

which is what we needed. QED

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