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
Oduvanchick [21]
3 years ago
9

When n=1 there is 1 dot. when n=2 there are 3 dots, when n=3 there are 6 dots. notice that the total number of dots increases by

n each time.
use induction to prove that
d(n)= n(n+1)/2

part A: prove the statement is true for n=1


part B: Assume that the statement is true for n=k + 1, therefor proving it true for all natural numbers, n.

hint* since the total number of dots increase by n each time, prove that d(k) + (k+1) = d (k+1)


*please answer i really need help!!

Mathematics
1 answer:
gayaneshka [121]3 years ago
6 0

Answer:

<h3>Part A</h3>
  • d(n) = n(n + 1)/2
  • n = 1 ⇒ d(1) = 1(1 + 1)/2 = 2/2 = 1, proved
<h3>Part B</h3>
  • d(k) + (k + 1) =
  • k(k + 1)/2 + (k + 1) =
  • [k(k + 1) + 2(k + 1)]/2 =
  • [(k + 1)(k + 1 + 1)]/2 =
  • d(k + 1)
  • Proved

You might be interested in
a construction company is replacing a window in a house. the window is currently 3 feet wide by 4 feet tall. The homeowner wants
horrorfan [7]
For this case, the first thing you should do is take into account the following unit conversion:
 1 foot = 12 inches
 Therefore, the perimeter of the new window is given by:
 p = 2w + 2l
 Where,
 w: width
 l: long
 Substituting values:
 p = 2 * (3 + ((4 1/2) / 12)) + 2 * (4 + ((4 1/2) / 12))
 p = 15.5 feet
 Answer:
 
The new perimeter of the window in feet is:
 
p = 15.5 feet
5 0
4 years ago
What is the difference between an approximate answer and exact answer
ASHA 777 [7]
An example would be  1/3  as an exact answer  and 0.33 as an approximate answer because 1/3 = 0.333.....  - a recurring decimal where there are an infinite number of 3's. 0.33 would be correct to the nearest hundredth.

Radicals are exact answers :- like  √2 , √5 .  Approximate value for √2 is 1.414
5 0
4 years ago
Read 2 more answers
Can you help me please
matrenka [14]

Answer:

U=76 and R=42 so they are not

if it's helpful ❤❤❤❤

THANK YOU

4 0
3 years ago
A boat goes downstream from one place to another in 9 hours. It covers the same distance upstream in 11 hours. If the speed of t
Evgen [1.6K]

Answer:

198 km

Step-by-step explanation:

The speed of the boat supposed to be x km/h

(x+2)*9 = (x-2)*11

9x + 18 = 11x – 22

2x = 40

X = 20

Distance between 2 places: (20 + 2) * 9 = 198 km

Or (20 – 2 ) * 11 = 198 km

6 0
4 years ago
ok the 100 point question is... if i am walking to work at 6:00 and it takes me three hours to get there, and jimmy walks to the
wariber [46]
9:00 tricky question also
4 0
4 years ago
Read 2 more answers
Other questions:
  • Which expression or value is equivalent to (8+2i)(8−2i)?
    7·1 answer
  • Evaluate the expression: |1 - 5|
    5·2 answers
  • 2x + 3y = 6
    11·2 answers
  • On field trips, there must be 2 chaperones for every 15 students. Which ratio correctly expresses the ratio of students to
    11·1 answer
  • I will give 25 points to whoever can explain this to me, I don't really need answers but they are appreciated.
    11·1 answer
  • 35% of 20kids are boys.How many boys are there?
    7·2 answers
  • What set of refections would carry trapezoid ABCD onto itself?
    14·2 answers
  • Simplify the following expresion. Classify the resulting polynomial 4x(x+1)-(3x-8)(x+4) A) quadratic monomial B) quadratic trino
    11·1 answer
  • &lt;) Madison is organizing a 10K race. She is ordering cases of bottled water for the runners.
    14·1 answer
  • Evaluate the expression (3-2i)(3-2i) and write the result in the form a+bi ,where a is the real part of your answer and bis the
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!