The sequence {Fn} described by F0 = 1, F1 = 1, and Fn+2 = Fn+Fn+1, if n ≥ 0, is called a Fibonacci sequence. Its terms occur nat

urally in many botanical species, particularly those with petals or scales arranged in the form of a logarithmic spiral. Consider the sequence {xn}, where xn = Fn+1/Fn. Assuming that lim --> infinity, xn=x exists, show that x=(1+underrot5)/2.

Mathematics

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Consider the area shown below. The height of the triangle is 8 and the length of its base is 3. We have used the notation Dh for

tester [12383]

Answer:

$\text{Riemann sum }=\sum \frac{3}{8}(8-h)Dh$

$\text{Area =}\int_{a}^{b} \frac{3}{8}(8-h)Dh$

Step-by-step explanation:

Given that the triangle's height measures 8 and the base length is 3, we can apply the concept of similar triangles to represent the base of the smaller triangle in relation to h.

The height of the smaller triangle will be $(8-h)$ .

Denote x as the base of the smaller triangle. Thus, by utilizing the properties of similar triangles, we can establish ratios of the corresponding sides as illustrated below:

$\frac{8-h}{x} =\frac{8}{3} \\x=\frac{3}{8}(8-h)$