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
What is the area of the shaded region?​
saveliy_v [14]

Answer:

<em>Answer is</em><em> </em><em>330</em>

Step-by-step explanation:

area \: of \: shaded \: region \:  = \pi {r}^{2}  - \pi( {x}^{2}  \\ here \: r = 11 \: cm \: and \: x = 4 \: cm \\ area \: of \: a \\ shaded \: regoin \:  = \pi( {r}^{2} -   {x}^{2} ) \\  = \pi( {11}^{2}  -  {4}^{2} ) \\  = \pi(121 - 16) \\  = \pi(105) \\  =  \frac{22}{7}  \times 105 \\  = 22 \times 15 \\  = 330  \: {cm}^{2}

<em>AREA</em><em> </em><em>OF</em><em> </em><em>SHADED</em><em> </em><em>REGION</em><em> </em><em>=</em><em>330</em>

<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>HAVE A NICE DAY</em><em>!</em>

<em>THANKS FOR GIVING ME THE OPPORTUNITY</em><em> </em><em>TO ANSWER YOUR QUESTION</em><em>. </em>

5 0
3 years ago
I AM GIVING AWAY 25 POINTS TO BEST ANSWER PLEASE HELP! I AM GIVING LOTS OF POINTS FOR THIS! Cube shaped boxes of tissue are ship
Vika [28.1K]
Try finding the area of the box and the container
Then divide the container's area by the tissue box

Hope this helps :)
4 0
3 years ago
Read 2 more answers
A triangle ABC is reflected across the y-axis and then translated 5 units down to triangle A'B'C'. How are the side lengths of t
Oksi-84 [34.3K]

Answer:

d, c, a, b

d= 32, 56

c = 34, 64

a = 85, 92

b = 23, 55

Step-by-step explanation:

3 0
2 years ago
Evaluate.<br> (-4)=<br> (-7) = 0<br> Please help ASAP!!
denis-greek [22]
  • Answer:

<em>(-4)³ = (-4)(-4)(-4) = 16(-4) = - 64</em>

<em>(-7)² = (-7)(-7) = 49</em>

<em>(-)×(-) = +</em>

<em>(-)×(+) = -</em>

4 0
3 years ago
Explain how you can tell that 31/33 is in simplest form
shtirl [24]
Well 31 is not able to go any were and it has to stay 31
3 0
3 years ago
Read 2 more answers
Other questions:
  • Six less then a number is equal to ten
    11·2 answers
  • Please help! USE 3.14 as Pi please!
    6·1 answer
  • State the correct polar coordinate for the graph shown. It is not the option selected.
    8·1 answer
  • Which angles are corresponding angles
    9·1 answer
  • Find the value of x. Round to the<br> nearest tenth.<br> 3<br> Х<br> 4<br> x = [?]
    5·1 answer
  • Solve each equation. For each step. Identify the property used.
    5·1 answer
  • Help pls i really need help
    11·2 answers
  • Ms. Walch works as a car salesperson. She earns a monthly base salary of $ 4,000 Plus $ 500 commission for each car she sells. H
    10·2 answers
  • Which function is graphed?<br>​
    15·1 answer
  • Help me please!<br><br>I don't understand this:(​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!