POSSIBLE POINTS: 11.76

(15-16) Consider the Infinite Geometric Series:

vodka [1.7K]

15 Answer: S₁ = 1 S₂ = 4 S₃ = 13 S₄ = 40 Sum = NO

Step-by-step explanation:

1 + 3 + 9 + 27 + ... $\implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}$

16 Answer: $\bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}$

Step-by-step explanation:

$\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}$

$\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}$

5 0

3 years ago

Given f(x)=2x2−5x−3 and g(x)=2x2+x . What is (fg)(x) ?

gizmo_the_mogwai [7]

Answer:

fourth option

Step-by-step explanation:

note that ( $\frac{f}{g}$ )(x)x) = $\frac{f(x)}{g(x)}$

$\frac{f(x)}{g(x)}$ = $\frac{2x^2-5x-3}{2x^2+x}$ ← factorise numerator/ denominator

= $\frac{(x-3)(2x+1)}{x(2x+1)}$ ← cancel the common factor (2x + 1)

= $\frac{x-3}{x}$ where x ≠ 0, - $\frac{1}{2}$

4 0

3 years ago

It takes Max 9 minutes to read 10 pages of his book. Which equation represents the

Ksju [112]

Answer:

y represents the pages, while x represents the minutes. for every y, there is 9/10 x, therefore the equation is y=9/10x

6 0

3 years ago

Read 2 more answers

There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance

Natali5045456 [20]

The answer is 7/69.

There are 8 black-haired children among 24 children. The probability of randomly selecting black haired children for the first time is:
P1 = 8/24 = 1/3

Now, there are 7 black-haired children left among 23 children. The probability of randomly selecting black haired children for the second time is:
P2 = 7/23

Since we want both of these events to occur together, we will multiply their probabilities:
P = P1 * P2 = 1/3 * 7/23 = 7/69

6 0

3 years ago

For the sequence <img src="https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%202n%2F%28n%2B1%29" id="TexFormula1" title="a_{n} = 2n/(n+1)"

Nat2105 [25]

Answer:

$a_{10}=\frac{20}{11}$