2 years ago

Write the sum in sigma notation. $ \noindent 1 - x + x^2 - x^3 + \cdot\cdot\cdot + {(-1)}^n x^n $

Mathematics

1 answer:

Neko [114]2 years ago

3 0

$1-x+x^2-x^3...+(-1)^nx^n=\sum\limits_{n=0}^{\infty}(-1)^nx^n=\sum\limits_{n=1}^{\infty}(-1)^{n-1}x^{n-1}$

You might be interested in

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your

Katyanochek1 [597]

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0

2 years ago

A plumber charges a $45 fee to make a house call and then $25 for each hour of labor. The plumber uses an equation in the form e

sasho [114]

M=slope
In this case the slope would be $25
y=mx+b
y=25x+45

Answer: m=25

5 0

2 years ago

Read 2 more answers

"There are 3 teams of 18 employees working today. Company policy says that we need to have 1 supervisor for every 8 employees on

lesya692 [45]

They need 6 supervisors

8 0

2 years ago

Read 2 more answers

A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the im

loris [4]

Answer:

Coordinates of Vertices of triangle ABC are A (-4,3) , B(4,4) and C(1,1).

As, DO is Dilation of Δ ABC by Scale factor of $\frac{1}{2}$ .

Vertices of A' B'C' are

$A'=(\frac{-4}{2},\frac{3}{2})=(-2,\frac{3}{2}), B'=(\frac{4}{2},\frac{4}{2})=(2,2), C'=(\frac{1}{2},\frac{1}{2})$

So, Image Δ A'B'C' will be smaller than the Pre image Δ ABC.

The two triangles will be congruent.

AO is Dilated by a factor of half , so A'O' will be half of AO.

So, correct Statements are

1. AB is parallel to A'B'.

2.DO,1/2(x, y) =

The distance from A' to the origin is half the distance from A to the origin.

$OA=\sqrt{(-4)^2+3^2}=\sqrt{25}=5\\\\ O'A'=\sqrt{2^2+(\frac{3}{2})^2}=\frac{5}{2}=2.5$

8 0

2 years ago

Read 2 more answers

What is the Value of the underlined digit 646,950

Jobisdone [24]

I'm sorry, but what digit is underlined?

4 0

2 years ago

Read 2 more answers