Round to the nearest tenth if necessary.

PLEASE HURRY 50 POINTS Answer Both parts and I will reward Brainliest

vlabodo [156]

We have:

$a_1=-3$

and:

$r=4$

so:

$$\sum\limits_{n=2}^5\,-3\cdot4^{n-1}=\sum\limits_{n=1}^5\,-3\cdot4^{n-1}-a_1=S_5-a_1=\frac{-3-(-3)\cdot 4^5}{1-4}-(-3)=$

$=\dfrac{-3-(-3)\cdot 1024}{-3}+3=\dfrac{-3(1-1024)}{-3}+3=1-1024+3=\boxed{-1020}$

It is a finite sum, so it is convergent.

6 0

3 years ago

Use series to verify that<br><br> <img src="https://tex.z-dn.net/?f=y%3De%5E%7Bx%7D" id="TexFormula1" title="y=e^{x}" alt="y=e^{

SVETLANKA909090 [29]

$y = e^x\\\\\displaystyle y = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y= 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \frac{d}{dx}\left( 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+\ldots\right)\\\\$

$\displaystyle y' = \frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{2!}\right) + \frac{d}{dx}\left(\frac{x^3}{3!}\right) + \frac{d}{dx}\left(\frac{x^4}{4!}\right)+\ldots\\\\\displaystyle y' = 0+1+\frac{2x^1}{2*1} + \frac{3x^2}{3*2!} + \frac{4x^3}{4*3!}+\ldots\\\\\displaystyle y' = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y' = e^{x}\\\\$

This shows that $y' = y$ is true when $y = e^x$

-----------------------

Note 1: A more general solution is $y = Ce^x$ for some constant C.
Note 2: It might be tempting to say the general solution is $y = e^x+C$ , but that is not the case because $y = e^x+C \to y' = e^x+0 = e^x$ and we can see that $y' = y$ would only be true for C = 0, so that is why $y = e^x+C$ does not work.

6 0

3 years ago

If you have 2 gallons of juice, how many quarts do you have

Alexeev081 [22]

Answer:

Yessssir OwO UnU UwU TwT =.= -.- :p :3 :c c: Ahhhh OOPS I GOT TOO DISTRACTED TO ANSWER UR QUESTION... if u have 2 gallons of juice u will have 8 quarts.

Step-by-step explanation:

dis is becuzzzz 4 quarts equal a gallon

so now times it by 2 by 2 because were doing 2 gallons not just one misssy :3

hope that helped bye byeessss UwU

6 0

3 years ago

Pat's pizza sells pizzas for $9 plus .50 for each topping added to get the total cost of the pizza. Which is the dependent varia

sashaice [31]

The dependent variable is the cost of the pizza.

The Independent variable (or what you manipulate) is the toppings of the pizza, and the dependent variable (or what changes because you manipulated something) is the total cost of the pizza

5 0

2 years ago

Could someone help me find the domain and range? Thank you

Sonja [21]

(-4,0) (-3,3) (-1,0) (0,-3) (1,-5) (3,0)
So, domain numbers are -4, -3, -1, 0, 1, 3
Range are 0, 3, -3,-5,
Just take the ordered pairs and the Xs is the domain and the Ys are the range

8 0

3 years ago