3. Given the points A(-24) and B17, -2), find the coordinates of the point P on directed line segment
AB in the ratio 1:2.
(3 Points)

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Ответ:

BornAdopted21

01.07.2022

Mathematics

0.25 Converges

Step-by-step explanation:

First, we need to expand our series so that we get the following:

$\sum _{n=1}^{\infty \:}\frac{n}{4^n}+\frac{1}{4^{n+1}}$

We can then use the series ratio test on each term. (L < 1 = absolutely convergent)

$\sum _{n=1}^{\infty \:}\frac{n}{4^n}$

$\lim_{n \to \infty} \frac{n}{4^{n}\\}$ =

⇒ converges

$\sum _{n=1}^{\infty \:}\frac{1}{4^n^+1}$

$\lim_{n \to \infty} \frac{n}{4^{n}^+1\\}$

⇒ converges

converges + converges

= converges

~Hope this helps! Once again, sorry if my explanation is a bit confusing~

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3. Given the points A(-24) and B17, -2), find the coordinates of the point P on directed line segmentAB in the ratio 1:2.(3 Points)