1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Neporo4naja [7]
3 years ago
9

Evaluate (1/3+1/4+...+1/2009)(1+1/2+...+1/2008)-(1+1/3+1/4+...+1/2009)(1/2+1/3+...+1/2008)

Mathematics
2 answers:
Umnica [9.8K]3 years ago
5 0

Answer: -2007/4018. hope it helped

omeli [17]3 years ago
3 0

Answer:

-2007/4018

Step-by-step explanation:

1. Given

(1/3+1/4+...+1/2009)(1+1/2+...1/2008) - (1+1/3+1/4+...+1/2009)(1/2+1/3+...+1/2008)

2. Set new variable

k = 1/3+1/4+...+1/2008

3. Rewrite the equation

(k+1/2009)(1+1/2+k) - (1+k+1/2009)(1/2+k)

4. Simplify

(k+1/2009)(k+3/2) - (k+2010/2009)(k+1/2)

5. Expand

[k^2 + (1/2009 + 3/2)k + (1/2009)(3/2)] - [k^2 - (2010/2009+1/2)k - (2010/2009)(1/2)]

6. Rewrite

(1/2009 + 3/2 - 2010/2009 - 1/2)k + (1/2009)(3/2) - (2010/2009)(1/2)

7. Simplify

(3/2 - 2009/2009 - 1/2)k + 1/2(3/2009-2010/2009)

8. Evaluate

0*k + 1/2(-2007/2009)

= -2007/4018

You might be interested in
Amber is starting a garden. She plants 2 flowers the first month. The next month, she plans three times more flowers (6 flowers)
Artist 52 [7]
This is a geometric progression problem. We can the general formula that can tell us how many flowers would be planted each month.
Let's write the terms that we know and see if we can find the pattern:

\begin{tabular}{lll}
Month & Number of flowers planted & Different form            \\
1     & 2                         & 2\cdot3^0 \\
2     & 6                         & 2\cdot3^1 \\
3     & 18                        & 2\cdot3^2 \\
4     & 54                        & 2\cdot3^3
\end{tabular}
\end{table}
The patern here is obvious. Let's write it down:
N=2\cdot3^{n-1}
This formula gives us a number of flowers planted in the n-th month.
6 0
3 years ago
Identify a solution to this system of equations -4x+3y=23, x-y=-7
Komok [63]

bearing in mind that a solution to a system of equations is where their graph intersect or meets, Check the picture below.

6 0
4 years ago
Can 29 be broken down to an even number
Novay_Z [31]
29 can not be broken down to an even number
8 0
4 years ago
What is the inverse of f(x)=(-2x+2)/(x+7)?
Nana76 [90]

By applying the concept of the inverse of a function and <em>algebraic</em> handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

<h3>How to find the inverse of a function</h3>

In this question we have a <em>rational</em> function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

x \to y

f(x) \to x

x = \frac{-2\cdot y + 2}{y+7}

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

g(x) = \frac{- 7\cdot x + 2}{x + 2}

By applying the concept of the inverse of a function and <em>algebraic</em> handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

To learn more on inverses: brainly.com/question/7181576

#SPJ1

4 0
2 years ago
What is the quotient of 8,187 ÷ 24?
adell [148]

Answer:

341.125

Step-by-step explanation:

8187/24

341.125

7 0
3 years ago
Other questions:
  • Im not sure how to take a negative and divided it by a positive
    9·1 answer
  • Please answer this multiple choice question only if you know it! 40 points and brainliest!
    15·2 answers
  • The area of the parallelogram below is ____ square meters.
    8·2 answers
  • Marjorie needs to earn a C in her Geology class. Her current test scores are 71,77, and 72. Her final exam is worth 6 test score
    9·1 answer
  • Which expressions are differences of squares?
    6·1 answer
  • What is the measure of one interior angle of the regular 32 gon?​
    13·1 answer
  • What is the measure of angle C
    5·1 answer
  • Help wit 19 ASAP WILL MARK BRAINLIST
    14·1 answer
  • Which of these relations are functions? Select all that apply.
    11·1 answer
  • Ben works at the Sudsy Scrubbers car wash. Last week, he recorded the number of cars he washed each day.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!