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
schepotkina [342]
3 years ago
8

1/1×3 + 1/3×5 + ... + 1/47×49 HELP PLZ

Mathematics
1 answer:
Natalka [10]3 years ago
3 0

Answer:

  24/49

Step-by-step explanation:

Let's add the terms and see if there's a pattern

  \dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}

Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...

  \dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}

Then it appears the sum of n terms is (n/(2n+1)). So, the sum of 24 terms is ...

  S_{24}=\dfrac{24}{2\times24+1}=\boxed{\dfrac{24}{49}}

You might be interested in
Find all real zeros of the function f(x)=-5x(x^2-49)(x-2)
german
The zeros are 0,7,-7,2
4 0
3 years ago
A restaurant will select 1 card from a bowl to win a free lunch, jimmy puts 10 cards in the bowl. The bowl has a total of 150 ca
Phantasy [73]

The odds of jimmy winning a free lunch is 0.066.

<h3>What is Probability ?</h3>

Probability is the likeliness of an event to happen.

It is given that

A restaurant will select 1 card from a bowl to win a free lunch,

jimmy puts 10 cards in the bowl.

The bowl has a total of 150 cards in it

The odds of jimmy winning a free lunch is given by

= No. of chances / Total Outcomes

= 10/150

= 1/15

= 0.066

Therefore the odds of jimmy winning a free lunch is 0.066.

To know more about Probability

brainly.com/question/11234923

#SPJ1

3 0
2 years ago
Shellie spent $10.56 on oranges that cost $0.88 per orange. How many oranges did she purchase?
vlada-n [284]
You have to do 10.56 plus 88 and you will have your answer
6 0
3 years ago
Find the surface area of this right circular cylinder. The radius is 3 meters and the length is 6 meters. Answers;; 18? m3 45? m
frozen [14]

2 \times (\pi \times  {3}^{2} ) + 6 \times (2\pi \times 3) \\  = 18\pi + 36\pi \\  = 54\pi \: ( {m}^{2} )
that is (2 of area of circle + area of square)
8 0
3 years ago
Identify which statement is true a. -0.3 greater than -0.3 (repeats) b. 7/8 is greater than 9/10 C. 1 2/3 greater than 1.7 D. -1
geniusboy [140]
A. -0.3 equals (=) -0.3 so that's false
B. 7/8 is less than (>) 9/10
C. 1 2/3 is less than (<) 1.7
D. -1.2 is less (<) 0.521
3 0
3 years ago
Other questions:
  • There are 4,200 adults in Lakeveiw. 3/8 of adults in adults in lake view do not have children. How many adults in lakeview have
    12·1 answer
  • A two-runway (one runway for landing, one runway for taking off) airport is being designed for propeller-driven aircraft. The ti
    13·1 answer
  • The equation of the line that has a slope of -1 and goes through (-3,0) is:
    14·1 answer
  • What is the equation of the quadratic function represented by this table?
    11·1 answer
  • Five 1 gallon jugs to cups and needs to hold fluid oz how many can he surve
    12·1 answer
  • Shari and Ana are playing games at an arcade. Shari has $37.50 and is playing $0.50 games. Ana has $42.75 and is playing $0.75 g
    12·2 answers
  • Find the slope of the line.. pls help me ill give brainliest. Its timed.
    14·1 answer
  • At Happy Pizza, an 8-inch pizza costs $6.00 and a 16-inch pizza costs $14.00. Which pizza is a better deal?​
    15·2 answers
  • What is the proper to do 81x400
    9·2 answers
  • Hallenge
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!