I didn’t see an image or anything but I looked it up and it said regular polygons, since they have the sides all the same length they must always be in the same proportions, and their interior angles are always the same.
Answer:
<u>The sequence is</u>
- 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...
Each term is the sum of the consecutive numbers from 1 to that number.
<u>The nth term is the sum of the first n numbers:</u>
- aₙ = 1 + 2 + 3 + ... + n
- aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
- aₙ = n(n + 1)/2
1) The number of circles in the nth pile is n(n + 1)/2
2) When n tends to infinity the number of circles tends to infinity
Arc tan ( 1/√3 ) = arc tan ( √3/3 ) = 30°
180° = π ( in radians )
30° = 180°/6 = π/6
All of these sets meet the requirements of the triangle inequality. The sum of any two numbers in the set is greater than the third one. (You really only need to check that the sum of the smallest two is greater than the largest.)
It can help to resolve the numbers that are only indicated as to value.
√13 ≈ 3.606
2√10 ≈ 6.325
_____
Your comparisons can be ...
2 + 3 = 5 > 3.606 . . . is a triangle
5 + 5 = 10 > 6.325 . . . . . . is a triangle
5 + 12 = 17 > 15 . . . . . . . . is a triangle
Answer:
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