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
Aliun [14]
3 years ago
13

Find the sum of all positive integers less than 100, which:

Mathematics
1 answer:
wlad13 [49]3 years ago
3 0

Answer:

The sum of all positive integers less than 100, which are not divisible by 3 is 3267.

Step-by-step explanation:

The all positive integers less than 100 has sum, given by

S₁ = 1 + 2 + 3 + 4 + ......... + 99

⇒ S₁ = \frac{99 \times (99 + 1)}{2} = 4950

Now, the sum of all positive integers less than 100 which are divisible by 3 is

S₂ = 3 + 6 + 9 + 12 + 15 + ........ + 99

⇒ S₂ = 3(1 + 2 + 3 + ........ + 33)

⇒ S₂ = 3 \times \frac{33 \times (33 + 1)}{2} = 1683

Therefore, the sum of all positive integers less than 100, which are not divisible by 3 is = S₁ - S₂ = 4950 - 1683 = 3267. (Answer)

Note : The sum of n natural numbers S is given by

S = 1 + 2 + 3 + 4 + ....... + n = \frac{n \times (n + 1)}{2} .

You might be interested in
Write the fraction 45/54 in simplest form
icang [17]

Answer: 5/6

Step-by-step explanation:

Find the greatest common factor. I’m this case, the greatest common factor is 9. Now divide both the numerator and denominator by 9. You would get 5/6

7 0
3 years ago
Read 2 more answers
Which quadrilateral and why?
Zigmanuir [339]
Personally you can’t measure you have to be in person but just double it on a piece of paper and you’ll find it out
6 0
3 years ago
Normally, a car wash costs $6. Today, Marie found a coupon so she only has to pay 60% of the normal amount. How much will Marie
Snezhnost [94]
Marie will pay $3.60
7 0
3 years ago
Can you please help you have to type in a number her is the screenshot
lyudmila [28]

Answer:

Step-by-step explanation:

Rate = (20½ pounds)/(4 hours) = (5⅛ pounds)/hour

9 hours × (5⅛ pounds)/hour = 46⅛ pounds

4 0
3 years ago
Given the side lengths determine if the following triangles exist, if they do classify
katrin2010 [14]

Answer:

no

Step-by-step explanation:

no

5 0
3 years ago
Other questions:
  • Javier used the expression below to represent his score in a game of mini-golf.
    6·2 answers
  • Simone has 32 erasers. She arranges the erasers into 5
    11·1 answer
  • PLEASE, Help ASP
    5·1 answer
  • What is the radius of a circle if its area is 120 in2? (Round your answer to the nearest hundredth of an inch)
    8·1 answer
  • Explain why the absolute value of a number is always positive
    7·1 answer
  • A girl has a square pool with an area of 81 square feet and she adds a patio which is 3 feet wide around the pool what is the to
    5·1 answer
  • Choose the best definition for the following term:substitution
    15·2 answers
  • Plz help algebrA give points for it
    8·1 answer
  • PLEASE HEP ME WITH THIS ONE
    12·1 answer
  • Raul bought 45 shares of stock for $36 a share. He sold one year later for $38 a share. What was his percentage return?​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!