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Sauron [17]
3 years ago
15

Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair whic

h becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in the nth month? show that the answer is fn, where {fn} is the Fibonacci sequence defined in Example 3(c)
Let an= fn+1/fn and show that an-1=1+1/an-2.Assuming that{an} is convergent, find its limit.
Mathematics
1 answer:
docker41 [41]3 years ago
5 0

Answer:

Let f_n be the number of rabbit pairs at the beginning of each month. We start with one pair, that is f_1 = 1. After one month the rabbits still do not produce a new pair, which means f_2 = 1. After two months a new born pair appears, that is f_3 = 2, and so on. Let now n \geq 3 be any natural number. We have that f_n is equal to the previous amount of pairs f_n-1 plus the amount of new born pairs. The last amount is f_n-2, since any two month younger pair produced its first baby pair. Finally we have  

f_1 = f_2 = 1,f_n = f_n-1 + f_n-2 for any natural n  \geq 3.  

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m∠BCD = 145°  ⇒  m∠BCA = 180° - 145° = 35°

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3 years ago
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Each piece is 4/5 m long

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3 years ago
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What is the equation of the line that passes through (-3, -1) and has a slope of 2/5? Put your answer in slope-intercept form.
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The general formula of A line in slope-intercept form is the following:
y = mx + n

In this formula m represents the slope of the line. Therefore, we can conclude that m = 2/5.
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We also know that the line passes through the point (-3, -1) and we can therefore substitute this coordinate into the formula of the line.
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Multiply first.
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And finally add 1 1/5 to both sides of the equation.
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We can now switch sides.
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Now we've found our value of n, which we can substitute into the formula of our line. Hence, in slope-intercept form, we find the following:
y =  \frac{2}{5}  x  +  \frac{1}{5}

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