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
sattari [20]
3 years ago
7

Write the following sum using summation notation -2/5+3/6-4/7........11/14

Mathematics
1 answer:
horrorfan [7]3 years ago
3 0

Answer:

\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )

Step-by-step explanation:

Given: \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}

To write: the given expression using summation notation

Solution:

Summation notation helps to write a long sum as a single expression.

In the summation notation, the variable \sum is called the index of summation.

Let x_1,x_2,x_3,...,x_n denote a set of n numbers.

Then in summation notation,

x_1+x_2+x_3+...+x_n=\sum_{i=1}^{n}x_i

\frac{-2}{5}=(-1)^1\left ( \frac{1+1}{1+4} \right )\\\frac{3}{6}=(-1)^2\left ( \frac{2+1}{2+4} \right )\\\frac{-4}{7}=(-1)^3\left ( \frac{3+1}{3+4} \right )\\.\\.\\.\\\frac{11}{14}=(-1)^10\left ( \frac{10+1}{10+4} \right )\\\therefore \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}=\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )

You might be interested in
What unit of time or volume is 1 equals 2?
Ugo [173]
What exactly are you asking?
5 0
3 years ago
A colleague has been tutoring six students in 11th grade to prepare for the ACT. This colleague has asked you to evaluate the pe
marissa [1.9K]

We have been given that a colleague has been tutoring six students in 11th grade to prepare for the ACT. Student scores were as follows: 20, 18, 16, 15, 23, 20. We are asked to find the mean of the ACT scores.

We will use mean formula to solve our given problem.  

\text{Mean}=\frac{\text{Sum of terms}}{\text{Number of terms}}

\text{Mean}=\frac{20+18+16+15+23+20}{6}

\text{Mean}=\frac{112}{6}

\text{Mean}=18.66666

Upon rounding to nearest whole number, we will get:

\text{Mean}\approx 19

Therefore, the mean of the ACT scores is 19 and option 'c' is the correct choice.

5 0
3 years ago
Which set of ordered pairs represents y as a function of X? a{(-9, 2), (0, 6), (1, -2), (-3, 6)} b{(-1,0), (4, 3), (-7, -3), (-1
olga nikolaevna [1]
A is your answer

Explanation:

When dealing with functions, x’s never repeat.
8 0
3 years ago
Need your help in trigonometry! please help
iren2701 [21]

Answer:

Step-by-step explanation:

6 0
3 years ago
Help<br> I neeed to get this question right
Irina18 [472]

Answer:

6/10 is greater than 6/100

Step-by-step explanation:

6/10 = 3/5

6/100 = 3/50

3 fifties is lot more than 3 with 5 parts

hope it makes sense

5 0
3 years ago
Other questions:
  • Picture included
    13·2 answers
  • Express $112 for 14 hours as a unit rat
    7·2 answers
  • Which equation represents a line with a slope of zero?
    15·2 answers
  • Find the surface area of the cone in terms of pie
    9·1 answer
  • What is the recursive rule for the sequence -22.7, -18.4, -14.1, -9.8, -5.5
    13·2 answers
  • Job A pays $19.94 per hour. Job B pays $18.76 per hour, and this job has health
    8·1 answer
  • A taxicab charges an initial fee of $2.50, then charges $0.75 per mile traveled. How
    15·1 answer
  • How do I do this 20 points to whoever completes this.
    9·1 answer
  • Х
    13·1 answer
  • Iready solve percent problems
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!